A293493 E.g.f.: exp(x/(1 - x^3)).

1, 1, 1, 1, 25, 121, 361, 5881, 62161, 365905, 5145841, 84831121, 812318761, 11450816521, 243450591385, 3371056121161, 51784222133281, 1275605799044641, 23531635543402081, 410559590525890465, 11089633716053137081, 256375957896260034841, 5161258224477109736521

Offset

0,5

Links

Table of n, a(n) for n=0..22.

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

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

Cf. A293494.

Sequence in context: A274783 A354553 A367719 * A356629 A362571 A198040

Adjacent sequences: A293490 A293491 A293492 * A293494 A293495 A293496

Keyword

nonn

Author

Seiichi Manyama, Oct 10 2017

Status

approved