{"id":2883,"date":"2023-05-24T18:11:06","date_gmt":"2023-05-24T10:11:06","guid":{"rendered":"https:\/\/www.shuizilong.com\/house\/?p=2883"},"modified":"2023-05-24T18:14:29","modified_gmt":"2023-05-24T10:14:29","slug":"%e6%97%a0%e6%a0%87%e5%8f%b7%e8%bf%9e%e9%80%9a%e5%9b%be","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/%e6%97%a0%e6%a0%87%e5%8f%b7%e8%bf%9e%e9%80%9a%e5%9b%be\/","title":{"rendered":"\u65e0\u6807\u53f7\u8fde\u901a\u56fe"},"content":{"rendered":"<ul>\n<li><a href=\"https:\/\/oeis.org\/A001349\">https:\/\/oeis.org\/A001349<\/a><\/li>\n<li><a href=\"https:\/\/mathworld.wolfram.com\/EulerTransform.html\">Weisstein, Eric W. &#8220;Euler Transform.&#8221; From MathWorld&#8211;A Wolfram Web Resource.<\/a><\/li>\n<li><a href=\"https:\/\/www.luogu.com.cn\/blog\/Karry5307\/solution-p5900\">\u9898\u89e3 P5900 \u3010\u65e0\u6807\u53f7\u65e0\u6839\u6811\u8ba1\u6570\u3011<\/a><\/li>\n<\/ul>\n<p>\u6ca1\u627e\u5230\u76f8\u5173\u7684\u9898\u76ee0.0.<\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\n#include &lt;lastweapon\/poly&gt;\r\n#include &lt;lastweapon\/number&gt;\r\n\r\nusing namespace lastweapon;\r\n\r\nconst int N = int(1e2) + 9;\r\nVVI Partition; VI cur;\r\nint n, m;\r\n\r\nvoid gen(int n, int s = 1){\r\n    if (!n){\r\n        Partition.PB(cur);\r\n    }\r\n    else if (n &gt;= s){\r\n        cur.PB(s); gen(n-s, s); cur.pop_back();\r\n        gen(n, s+1);\r\n    }\r\n}\r\n\r\nMint c(const VI P, int n){\r\n    Mint z = fac&#x5B;n]; int c = 0, l = P.front();\r\n    ECH(it, P){\r\n        z \/= *it; if (*it != l){\r\n            z *= invFac&#x5B;c]; l = *it;\r\n            c = 1;\r\n        }\r\n        else{\r\n            ++c;\r\n        }\r\n    }\r\n\r\n    z *= invFac&#x5B;c];\r\n    return z;\r\n}\r\nint g(const VI P){\r\n    int z = 0; REP(i, SZ(P)){\r\n        z += P&#x5B;i] \/ 2; REP(j, i) z += __gcd(P&#x5B;i], P&#x5B;j]);\r\n    }\r\n    return z;\r\n}\r\n\r\nconst int PMAX = int(1e2) + 9;\r\nVI P; bitset&lt;PMAX&gt; isP; int mu&#x5B;PMAX];\r\nvoid sieve(){\r\n    mu&#x5B;1] = 1; FOR(i, 2, PMAX){\r\n        if (!isP&#x5B;i]) P.PB(i), mu&#x5B;i] = -1;\r\n        for (int j=0;j&lt;SZ(P)&amp;&amp;i*P&#x5B;j]&lt;PMAX;++j){\r\n            isP&#x5B;i*P&#x5B;j]]=1; if (!(i%P&#x5B;j])){\r\n                mu&#x5B;i*P&#x5B;j]] = 0;\r\n                break;\r\n            } else{\r\n                mu&#x5B;i*P&#x5B;j]] = -mu&#x5B;i];\r\n            }\r\n        }\r\n    }\r\n}\r\n\r\nint main(){\r\n\r\n#ifndef ONLINE_JUDGE\r\n    \/\/freopen(&quot;in.txt&quot;, &quot;r&quot;, stdin);\r\n    \/\/freopen(&quot;out.txt&quot;, &quot;w&quot;, stdout);\r\n#endif\r\n\r\n    sieve();\r\n\r\n    m = 2; n = 21;\r\n\r\n    Poly a(n), b(21);\r\n\r\n    FOR(i, 1, n) {\r\n        Partition.clear(); gen(i);\r\n        Mint z = 0; ECH(it, Partition) {\r\n            z += c(*it, i) * pow(Mint(m), g(*it));\r\n        }\r\n        z *= invFac&#x5B;i];\r\n        b&#x5B;i] = z;\r\n    }\r\n\r\n    Poly c(n);\r\n\r\n    FOR(i, 1, n) {\r\n        c&#x5B;i] = i * b&#x5B;i];\r\n        REP_1(j, i-1) c&#x5B;i] -= c&#x5B;j] * b&#x5B;i-j];\r\n    }\r\n\r\n    FOR(i, 1, n) {\r\n        REP_1(d, i) if (i % d == 0) {\r\n            a&#x5B;i] += mu&#x5B;i\/d] * c&#x5B;d];\r\n        }\r\n        a&#x5B;i] \/= i;\r\n    }\r\n\r\n    FOR(i, 1, n) {\r\n        cout &lt;&lt; a&#x5B;i] &lt;&lt; &quot; &quot;;\r\n    }\r\n    cout &lt;&lt; endl;\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>https:\/\/oeis.org\/A001349 Weisstein, Eric W. &#8220;Euler Transform.&#8221; From MathWorld&#8211;A Wolfram Web Resource. \u9898\u89e3 P5900 \u3010\u65e0\u6807\u53f7\u65e0\u6839\u6811\u8ba1\u6570\u3011 \u6ca1\u627e\u5230\u76f8\u5173\u7684\u9898\u76ee0.0. #include &lt;lastweapon\/poly&gt; #include &lt;lastweapon\/number&gt; using namespace lastweapon; const int N = int(1e2) + 9; VVI Partition; VI cur; int n, m; void gen(int n, int s = 1){ if (!n){ Partition.PB(cur); } else if (n &gt;= s){ cur.PB(s); gen(n-s, s); [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1],"tags":[],"class_list":["post-2883","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-Kv","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2883","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=2883"}],"version-history":[{"count":2,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2883\/revisions"}],"predecessor-version":[{"id":2885,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2883\/revisions\/2885"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=2883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=2883"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=2883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}