A353222 Expansion of e.g.f. (1 - x^3)^(-1/x).

1, 0, 2, 0, 12, 60, 120, 2520, 15120, 90720, 1693440, 13305600, 140374080, 2724321600, 27744837120, 414096883200, 8689288608000, 111399326438400, 2114134793971200, 48501156601497600, 759659036405068800, 17279306372135808000, 434100706059205785600

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..floor((n+1)/3)} (3*k-1)/k * a(n-3*k+1)/(n-3*k+1)!.

a(n) ~ sqrt(2*Pi) * n^(n + 1/2) / (3*exp(n)). - Vaclav Kotesovec, May 04 2022

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x^3)^(-1/x)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-log(1-x^3)/x)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, (i+1)\3, (3*j-1)/j*v[i-3*j+2]/(i-3*j+1)!)); v;

Crossrefs

Cf. A121452, A353224.

Cf. A246689, A353223.

Sequence in context: A182437 A326860 A013316 * A013310 A269889 A293567

Adjacent sequences: A353219 A353220 A353221 * A353223 A353224 A353225

Keyword

nonn

Author

Seiichi Manyama, May 01 2022

Status

approved