A354243 Expansion of e.g.f. Sum_{k>=0} (2*k)! * log(1+x)^k / k!.

1, 2, 22, 652, 36252, 3249648, 427841136, 77725790784, 18629187576192, 5694658698037824, 2162203542669622464, 998275836346954738560, 550745779092109449586560, 357819370067278253918223360, 270404811566689476740771496960

Offset: 0

Author

Seiichi Manyama, May 20 2022

Keywords

• nonn

Crossrefs

Cf. A006252, A354250.

Cf. A316747, A354240, A354244.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (2*k)!*log(1+x)^k/k!)))

PARI

a(n) = sum(k=0, n, (2*k)!*stirling(n, k, 1));

Formula

a(n) = Sum_{k=0..n} (2*k)! * Stirling1(n,k).