A380018 Expansion of e.g.f. 1/(exp(-4*x) - 4*x)^(1/4).

1, 2, 16, 256, 5856, 175296, 6486016, 285756416, 14606007296, 849615763456, 55415153442816, 4005309938466816, 317750919017168896, 27449350209163821056, 2564871898004949303296, 257753802183061443444736, 27720748513211258671988736, 3176821722223524679312736256

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = n! * Sum_{k=0..n} (-4)^k * (4*k+1)^(n-k) * binomial(-1/4,k)/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (-4)^k*(4*k+1)^(n-k)*binomial(-1/4, k)/(n-k)!);

Crossrefs

Cf. A072597, A380014, A380016.

Sequence in context: A009044 A019318 A090727 * A108242 A140307 A114039

Adjacent sequences: A380015 A380016 A380017 * A380019 A380020 A380021

Keyword

nonn

Author

Seiichi Manyama, Jan 09 2025

Status

approved