A383380 Expansion of e.g.f. exp(-2*x) / (1-x)^4.

1, 2, 8, 40, 248, 1808, 15136, 142784, 1496960, 17254144, 216740864, 2945973248, 43065951232, 673626675200, 11224114860032, 198447384666112, 3710328985124864, 73136238041563136, 1515739708283944960, 32947698735175172096, 749499782353468522496, 17806903161183314378752

Offset

0,2

Links

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A000255.

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

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

a(n) ~ sqrt(Pi) * n^(n + 7/2) / (3*sqrt(2)*exp(n+2)). - Vaclav Kotesovec, Apr 25 2025

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-2*x)/(1-x)^4))

Crossrefs

Cf. A000261, A383344, A383378.

Cf. A000023, A052124, A087981, A383381.

Cf. A000255.

Sequence in context: A259869 A381346 A321733 * A371313 A000828 A296676

Adjacent sequences: A383377 A383378 A383379 * A383381 A383382 A383383

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 24 2025

Status

approved