A377803 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - log(1-3*x) / 3) ).

1, 1, 5, 51, 798, 16914, 453294, 14704542, 560274336, 24529661568, 1213557885720, 66956662956600, 4076440417367856, 271472012197547472, 19631093304600307152, 1531919987372848152240, 128314172533501646058240, 11482569303348317402868480, 1093343670892117401737893632

Offset: 0

Author

Seiichi Manyama, Nov 08 2024

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A138013, A377737.

Cf. A352069, A370907, A370939, A377790.

Programs

PARI

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

PARI

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

Formula

a(n) = n! * Sum_{k=0..n} 3^(n-k) * |Stirling1(n,k)|/(n-k+1)!.