A380016 Expansion of e.g.f. 1/(exp(-3*x) - 3*x)^(1/3).

1, 2, 13, 161, 2833, 64841, 1827685, 61192181, 2372620801, 104549934977, 5160225776101, 281994042839477, 16902276273364465, 1102519010117525105, 77749077431938305541, 5894145002422856684501, 478015727336387513545345, 41295912476641866286397825, 3786025873450493919700627525

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * Sum_{k=0..n} (-3)^k * (3*k+1)^(n-k) * binomial(-1/3,k)/(n-k)!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (-3)^k*(3*k+1)^(n-k)*binomial(-1/3, k)/(n-k)!);

Crossrefs

Cf. A072597, A380014, A380018.

Sequence in context: A062593 A347051 A291140 * A192563 A014507 A132614

Adjacent sequences: A380007 A380014 A380015 * A380017 A380018 A380019

Keyword

nonn,new

Author

Seiichi Manyama, Jan 09 2025

Status

approved