A383344 Expansion of e.g.f. exp(-4*x) / (1-x)^4.

1, 0, 4, 8, 72, 416, 3520, 31104, 316288, 3525632, 43117056, 572195840, 8191304704, 125761056768, 2060841582592, 35894401335296, 662066514984960, 12890305925218304, 264155723747688448, 5682905054074109952, 128051031032232411136, 3015653024970577018880

Offset

0,3

Links

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

Formula

a(n) = n! * Sum_{k=0..n} (-4)^(n-k) * binomial(k+3,3)/(n-k)!.

a(n) = (n-1) * (a(n-1) + 4*a(n-2)) for n > 1.

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A000166.

a(n) ~ sqrt(2*Pi) * n^(n + 7/2) / (6*exp(n+4)). - Vaclav Kotesovec, Apr 25 2025

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-4*x)/(1-x)^4))

Crossrefs

Column k=4 of A295181.

Cf. A000166, A087981, A137775.

Cf. A088991, A381504.

Sequence in context: A013112 A274461 A240503 * A221484 A338314 A288956

Adjacent sequences: A383341 A383342 A383343 * A383345 A383346 A383347

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 23 2025

Status

approved