A380208 Expansion of e.g.f. exp( (1+3*x)^(1/3) - 1 ).

1, 1, -1, 5, -39, 421, -5809, 97609, -1933455, 44107881, -1138752449, 32820576141, -1044523471991, 36379398867085, -1376300966184689, 56200996031812241, -2463713702730471199, 115400572452587463249, -5751849729149085927425, 303954806150664749166101

Offset

0,4

Links

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

Formula

a(n) = Sum_{k=0..n} 3^(n-k) * Stirling1(n,k) * Bell(k).

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((1+3*x)^(1/3)-1)))

Crossrefs

Cf. A000806, A373713, A380215, A380229.

Sequence in context: A308939 A317618 A024216 * A127189 A121354 A122486

Adjacent sequences: A380188 A380189 A380190 * A380209 A380210 A380211

Keyword

sign,new

Author

Seiichi Manyama, Jan 16 2025

Status

approved