cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A234628 Number of undirected cycles in the graph join C_n + C_n of cycle graphs.

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%I A234628 #30 Jan 10 2025 19:33:01
%S A234628 197,2766,60142,1921115,84779781,4939361970,367260392738,
%T A234628 33943163219867,3817771391967469,513555324752795822,
%U A234628 81424493891629268382,15029177059618712556883,3195217968081609415815677,775224832686819672474135234,212905295555773231486108386402
%N A234628 Number of undirected cycles in the graph join C_n + C_n of cycle graphs.
%H A234628 Andrew Howroyd, <a href="/A234628/b234628.txt">Table of n, a(n) for n = 3..100</a>
%H A234628 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>.
%H A234628 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphJoin.html">Graph Join</a>.
%F A234628 a(n) = 2 + n^2*(-1 + Sum_{k=1..n} ((k-1)!*B(n,k))^2/k)/2, where B(n,k) = [x^n][y^k] 1/(1 - x*y*(2/(1 - x) - 1)/(1 - x)). - _Andrew Howroyd_, Jan 10 2025
%o A234628 (PARI) B(n)=polcoef(1/(1 - x*y*(2/(1 - x) - 1)/(1 - x)) + O(x*x^n), n)
%o A234628 a(n)={my(v=Vecrev(B(n))); (sum(k=1, n, (n*v[1+k]/k)^2*k!*(k-1)!) + 4 - n^2)/2} \\ _Andrew Howroyd_, Jan 10 2025
%Y A234628 Cf. A137891.
%K A234628 nonn
%O A234628 3,1
%A A234628 _Eric W. Weisstein_, Dec 28 2013
%E A234628 Name corrected by _Eric W. Weisstein_, Mar 09 2016
%E A234628 a(11)-a(15) from _Max Alekseyev_, Dec 30 2024
%E A234628 a(2) removed and a(16) onwards added by _Andrew Howroyd_, Jan 10 2025