OFFSET
0,3
FORMULA
E.g.f.: Series_Reversion( (1 - x)^2 * log(1+x) ).
a(n) = Sum_{k=1..n} (2*n+k-2)!/(2*n-1)! * Stirling2(n,k).
a(n) ~ 2^(n-1) * LambertW(exp(1/2))^(2*n-1) * n^(n-1) / (sqrt(LambertW(exp(1/2)) + 1) * exp(n) * (2*LambertW(exp(1/2))-1)^(3*n-1)). - Vaclav Kotesovec, Mar 29 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)^2*log(1+x)))))
(PARI) a(n) = sum(k=1, n, (2*n+k-2)!/(2*n-1)!*stirling(n, k, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 20 2024
STATUS
approved