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

0,2

Links

Table of n, a(n) for n=0..14.

Formula

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

a(n) ~ sqrt(Pi) * 2^(2*n+1) * n^(2*n + 1/2) / exp(2*n + 1/8). - Vaclav Kotesovec, Jan 24 2026

Mathematica

Table[Sum[(2*k)!*StirlingS1[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 24 2026 *)

Prog

(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));

Crossrefs

Cf. A006252, A354250.

Cf. A316747, A354240, A354244.

Sequence in context: A177042 A308535 A318639 * A220732 A333796 A132568

Adjacent sequences: A354240 A354241 A354242 * A354244 A354245 A354246

Keyword

nonn

Author

Seiichi Manyama, May 20 2022

Status

approved