A383382 Expansion of e.g.f. exp(-3*x) / (1-x)^5.

1, 2, 9, 48, 321, 2502, 22329, 223668, 2481921, 30187242, 399071529, 5694475608, 87197543361, 1425766728942, 24787205125209, 456477484618908, 8875541469155841, 181670665706512722, 3904395263350689609, 87898121215165479168, 2068411075529464370241, 50778930934558144895382

Offset

0,2

Links

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

Formula

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

a(0) = 1, a(1) = 2; a(n) = (n+1)*a(n-1) + 3*(n-1)*a(n-2).

a(n) ~ sqrt(2*Pi) * n^(n + 9/2) / (24*exp(n+3)). - Vaclav Kotesovec, Apr 25 2025

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[-3x]/(1-x)^5, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 31 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-3*x)/(1-x)^5))

Crossrefs

Cf. A001909, A383381, A383383, A383384.

Cf. A010843, A137775, A383378.

Sequence in context: A052826 A358264 A375795 * A246759 A191005 A257544

Adjacent sequences: A383379 A383380 A383381 * A383383 A383384 A383385

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 24 2025

Status

approved