OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..325
FORMULA
a(n) = (2*n)! * Sum_{k=n..2*n} (2*n+1-k) * |Stirling1(k,n)|/k!.
a(n) = [x^(2*n)] ((2*n)!/n!) * (-log(1 - x))^n/(1 - x)^2.
From Vaclav Kotesovec, Sep 23 2021: (Start)
a(n) = [x^n] Gamma(2*n + x + 2) / Gamma(x + 2).
a(n) ~ c * d^n * (n-1)!, where d = 8*w^2/(2*w-1), w = -LambertW(-1,-exp(-1/2)/2) and c = 1.5967712192197964362930380385801737624829174112909160160618... (End)
PROG
(PARI) a(n) = (2*n)!*polcoef(sum(k=n, 2*n, binomial(x+k, k)), n);
(PARI) a(n) = (2*n)!*sum(k=n, 2*n, (2*n+1-k)*abs(stirling(k, n, 1))/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 23 2021
STATUS
approved