A189423 Expansion of e.g.f. exp(log(1+x) + log(1+x)^2).

1, 1, 2, 0, 10, -50, 368, -3052, 28740, -302220, 3508152, -44532048, 613399752, -9109006920, 145029146208, -2463935369040, 44482964644368, -850291412311152, 17153458120885152, -364163960169826944, 8114899768747511712

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..447

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties , arXiv:1103.2582 [math.CO], 2011-2013.

Formula

a(0) = 1; a(n) = Sum_{m=1..n} Sum_{k=m..n} k!*binomial(m,k-m)*stirling1(n,k))/m! for n>0.

a(n) = Sum_{k=0..n} A047974(k) * Stirling1(n,k). - Seiichi Manyama, May 14 2022

Prog

(Maxima)
a(n):=sum(sum(k!*binomial(m, k-m)*stirling1(n, k), k, m, n)/m!, m, 1, n);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(log(1+x)*(1+log(1+x))))) \\ Seiichi Manyama, May 14 2022
(PARI) a(n) = sum(k=0, n, k!*sum(j=0, k\2, 1/(j!*(k-2*j)!))*stirling(n, k, 1)); \\ Seiichi Manyama, May 14 2022

Crossrefs

Cf. A005444, A047974.

Sequence in context: A167387 A368956 A035237 * A342287 A230696 A138542

Adjacent sequences: A189420 A189421 A189422 * A189424 A189425 A189426

Keyword

sign

Author

Vladimir Kruchinin, Apr 21 2011

Status

approved