A375226 Expansion of e.g.f. exp( (x / (1-x))^3 ) / (1-x)^2.

1, 2, 6, 30, 240, 2520, 30600, 413280, 6168960, 101666880, 1842825600, 36483955200, 782548905600, 18048500870400, 444816333561600, 11656620213638400, 323500679915212800, 9475966585948262400, 292101319958063616000, 9450373008137757696000

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^3)/(1-x)^2))
(PARI) a(n) = n!*sum(k=0, n\3, binomial(n+1, n-3*k)/k!);

Crossrefs

Cf. A361595, A375227.

Sequence in context: A027882 A306782 A106209 * A003266 A303169 A369198

Adjacent sequences: A375223 A375224 A375225 * A375227 A375228 A375229

Keyword

nonn

Author

Seiichi Manyama, Aug 06 2024

Status

approved