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URL: https://oeis.org/A234628

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A234628
Number of undirected cycles in the graph join C_n + C_n of cycle graphs.
2
197, 2766, 60142, 1921115, 84779781, 4939361970, 367260392738, 33943163219867, 3817771391967469, 513555324752795822, 81424493891629268382, 15029177059618712556883, 3195217968081609415815677, 775224832686819672474135234, 212905295555773231486108386402
OFFSET
3,1
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle.
Eric Weisstein's World of Mathematics, Graph Join.
FORMULA
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
PROG
(PARI) B(n)=polcoef(1/(1 - x*y*(2/(1 - x) - 1)/(1 - x)) + O(x*x^n), n)
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
CROSSREFS
Cf. A137891.
Sequence in context: A201256 A231462 A188361 * A329107 A097733 A114050
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 28 2013
EXTENSIONS
Name corrected by Eric W. Weisstein, Mar 09 2016
a(11)-a(15) from Max Alekseyev, Dec 30 2024
a(2) removed and a(16) onwards added by Andrew Howroyd, Jan 10 2025
STATUS
approved