A375722 Expansion of e.g.f. 1 / (1 + 3 * log(1 - x))^3.

1, 9, 117, 1962, 40122, 966276, 26755812, 836862192, 29167596504, 1120629465432, 47044646845848, 2142210019297680, 105154320625284240, 5534780654854980000, 310945503593770489440, 18570787974013838515200, 1174884522886771261079040

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = (1/2) * Sum_{k=0..n} 3^k * (k+2)! * |Stirling1(n,k)|.

a(0) = 1; a(n) = 3 * Sum_{k=1..n} (2*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+3*log(1-x))^3))
(PARI) a(n) = sum(k=0, n, 3^k*(k+2)!*abs(stirling(n, k, 1)))/2;

Crossrefs

Cf. A354263, A375721.

Cf. A354122, A367475.

Cf. A367473.

Sequence in context: A113344 A305968 A367473 * A081629 A051617 A358387

Adjacent sequences: A375719 A375720 A375721 * A375723 A375724 A375725

Keyword

nonn

Author

Seiichi Manyama, Aug 25 2024

Status

approved