cp's OEIS Frontend

A234627 Numbers of undirected cycles in the n-sun graph.

%I A234627 #33 Feb 16 2025 08:33:21
%S A234627 1,3,11,44,198,1036,6346,45019,364039,3306553,33328389,369132782,
%T A234627 4456043300,58230679722,818965960156,12334276322245,198059886271741,
%U A234627 3377876368962559,60978094460613103,1161619710523459392
%N A234627 Numbers of undirected cycles in the n-sun graph.
%C A234627 Extended to n=1 and 2 using the closed-form sum. - _Eric W. Weisstein_, May 04 2017
%H A234627 Andrew Howroyd and Vaclav Kotesovec, <a href="/A234627/b234627.txt">Table of n, a(n) for n = 1..420</a> (terms 3..50 from Andrew Howroyd; terms 1..2 corrected by _Georg Fischer_, Jan 20 2019)
%H A234627 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A234627 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SunGraph.html">Sun Graph</a>
%F A234627 a(n) = (1/2) * (2 - binomial(n+1, 2) + Sum_{k=1..n} (k-1)! * (binomial(n, k) + Sum_{j=1..k} Sum_{i=0..n-j-k} n*(2^j)*binomial(n-j-i-1, j-1)*binomial(i+j-1, i)*binomial(n-2*j-i, k-j)/j) ). - _Andrew Howroyd_, Mar 05 2016
%F A234627 a(n) ~ exp(3)/2 * (n-1)!. - _Vaclav Kotesovec_, Mar 06 2016
%t A234627 Table[(2 - Binomial[n + 1, 2] + Sum[(k - 1)! (Binomial[n, k] + Sum[n 2^j Binomial[n - j - i - 1, j - 1] Binomial[i + j - 1, i] Binomial[n - 2 j - i, k - j]/j, {j, k}, {i, 0, n - j - k}]), {k, n}])/2, {n, 20}] (* _Eric W. Weisstein_, Dec 14 2017 *)
%o A234627 (PARI) a(n) = (2 - binomial(n+1, 2) + sum(k=1, n, (k-1)! * (binomial(n, k) + sum(j=1, k, sum(i=0, n-j-k, n*(2^j)*binomial(n-j-i-1, j-1)*binomial(i+j-1, i)*binomial(n-2*j-i, k-j)/j)))))/2; \\ after formula; _Michel Marcus_, Mar 06 2016
%Y A234627 Cf. A002807, A192856.
%K A234627 nonn
%O A234627 1,2
%A A234627 _Eric W. Weisstein_, Dec 28 2013
%E A234627 a(12)-a(14) from _Eric W. Weisstein_, Apr 09 2014
%E A234627 a(15)-a(20) from _Andrew Howroyd_, Mar 05 2016