OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..470
FORMULA
G.f.: Sum_{k>=0} (-x)^k / (1 - (3*k+1)*x)^(k+1).
a(n) = Sum_{k=0..n} (-1)^k * (3*k+1)^(n-k) * binomial(n,k).
a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * 3^(n-k) * Stirling2(n-k,k)/(n-k)!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(1-exp(3*x)))))
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (-x)^k/(1-(3*k+1)*x)^(k+1)))
(PARI) a(n) = sum(k=0, n, (-1)^k*(3*k+1)^(n-k)*binomial(n, k));
(PARI) a(n) = n!*sum(k=0, n\2, (-1)^k*3^(n-k)*stirling(n-k, k, 2)/(n-k)!);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 29 2022
STATUS
approved