A375672 Expansion of e.g.f. 1 / (1 + x * log(1 - x))^3.

1, 0, 6, 9, 168, 810, 11592, 103320, 1511808, 19350576, 315908640, 5127930720, 95386497984, 1843728194880, 38978317929600, 866801578406400, 20627303078937600, 516780346452733440, 13695223899883530240, 381043219813390540800, 11135125489382277811200

Offset: 0

Author

Seiichi Manyama, Aug 23 2024

Keywords

• nonn

Crossrefs

Cf. A052830, A375671.

Cf. A354122, A375661.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x))^3))

PARI

a(n) = n!*sum(k=0, n\2, (k+2)!*abs(stirling(n-k, k, 1))/(n-k)!)/2;

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A052830.

a(n) = (n!/2) * Sum_{k=0..floor(n/2)} (k+2)! * |Stirling1(n-k,k)|/(n-k)!.