OFFSET
0,3
FORMULA
a(n) = 1/(4*(n+1)) * Sum_{k=0..n+1} 3^(n+1-k) * k^n * binomial(n+1,k).
a(n) = n! * Sum_{k=0..n} 4^(n-k) * Stirling2(n,k)/(n-k+1)!. - Seiichi Manyama, Nov 07 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(4*x/(3+exp(4*x)))/x))
(PARI) a(n) = sum(k=0, n+1, 3^(n+1-k)*k^n*binomial(n+1, k))/(4*(n+1));
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Seiichi Manyama, Mar 05 2024
STATUS
approved