A375415 Expansion of e.g.f. exp(-x^3 * (1 - x)^2) / (1 - x).

1, 1, 2, 0, 48, 120, 1080, -2520, 100800, 120960, 6652800, -26611200, 1297296000, -778377600, 177989011200, -610248038400, 53004401049600, -62245299916800, 12760286482944000, -13009267682611200, 5173295797942272000, 3608804645462016000

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = (-1)^n * n! * Sum_{k=0..floor(n/3)} binomial(2*k-1,n-3*k)/k!.

Prog

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

Crossrefs

Cf. A375410, A375413.

Sequence in context: A319113 A158194 A326718 * A097173 A009493 A009718

Adjacent sequences: A375412 A375413 A375414 * A375416 A375417 A375418

Keyword

sign

Author

Seiichi Manyama, Aug 14 2024

Status

approved