A353895 Expansion of e.g.f. exp( (x * (exp(x) - 1))^3 / 36 ).

1, 0, 0, 0, 0, 0, 20, 210, 1400, 7560, 36120, 159390, 850300, 9875580, 170133964, 2688015330, 36706233200, 444802722000, 4939264076016, 52543545234534, 583037908936500, 7645631225897700, 124931080233222340, 2327407301807577066, 44282377224446369800

Offset

0,7

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = n! * Sum_{k=0..floor(n/6)} (3*k)! * Stirling2(n-3*k,3*k)/(36^k * k! * (n-3*k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((x*(exp(x)-1))^3/36)))
(PARI) a(n) = n!*sum(k=0, n\6, (3*k)!*stirling(n-3*k, 3*k, 2)/(36^k*k!*(n-3*k)!));

Crossrefs

Cf. A052506, A353894, A353896.

Cf. A327504, A353884, A353892.

Sequence in context: A074668 A139620 A094311 * A353884 A162640 A060853

Adjacent sequences: A353892 A353893 A353894 * A353896 A353897 A353898

Keyword

nonn

Author

Seiichi Manyama, May 09 2022

Status

approved