A353884 Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^3 / 36).

1, 0, 0, 0, 0, 0, 20, 210, 1400, 7560, 36120, 159390, 1035100, 17082780, 329893564, 5336661330, 73265956400, 889068944400, 9968073461616, 112902000191334, 1531070090032500, 27610559023112100, 586336131631313140, 12550716321612658266, 254052845940651258600

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 * (n-3*k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(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*(n-3*k)!));

Crossrefs

Cf. A052848, A353883, A353885.

Cf. A346894, A353881.

Sequence in context: A139620 A094311 A353895 * A162640 A060853 A010972

Adjacent sequences: A353881 A353882 A353883 * A353885 A353886 A353887

Keyword

nonn

Author

Seiichi Manyama, May 09 2022

Status

approved