OFFSET
0,5
FORMULA
E.g.f.: Product_{k>0} exp(x^(3*k-2)).
a(n) ~ exp(2*sqrt(3*n)/3 - n + 1/6) * n^(n-1/4) / (sqrt(2) * 3^(1/4)). - Vaclav Kotesovec, Oct 10 2017
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * (3*k+1)! * a(n-3*k-1). - Ilya Gutkovskiy, Feb 24 2022
a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k)/(n-3*k)!. - Seiichi Manyama, Jun 08 2024
PROG
(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(1-x^3))))
(PARI) N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(3*k-2)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 10 2017
STATUS
approved