OFFSET
3,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 3..100
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
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