A351793 Expansion of e.g.f. 1/(1 - x*exp(-4*x)).

1, 1, -6, 6, 248, -2120, -12144, 458416, -2194560, -102238848, 2116494080, 12999644416, -1291721856000, 14270887521280, 650218659514368, -24515781088389120, -89087389799317504, 27917287109308284928, -556978307357438705664, -23150337968775391281152

Offset

0,3

Links

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

Formula

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

a(0) = 1 and a(n) = n * Sum_{k=0..n-1} (-4)^(n-1-k) * binomial(n-1,k) * a(k) for n > 0.

Mathematica

a[0] = 1; a[n_] := n!*Sum[(-4*(n - k))^k/k!, {k, 0, n}]; Array[a, 20, 0] (* Amiram Eldar, Feb 19 2022 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(-4*x))))
(PARI) a(n) = n!*sum(k=0, n, (-4*(n-k))^k/k!);
(PARI) a(n) = if(n==0, 1, n*sum(k=0, n-1, (-4)^(n-1-k)*binomial(n-1, k)*a(k)));

Crossrefs

Column k=4 of A351791.

Cf. A336952.

Sequence in context: A123190 A244956 A239532 * A370711 A165641 A213149

Adjacent sequences: A351790 A351791 A351792 * A351794 A351795 A351796

Keyword

sign

Author

Seiichi Manyama, Feb 19 2022

Status

approved