A189424 Expansion of e.g.f exp(log(1+x)+2*log(1+x)^2).

1, 1, 4, 0, 44, -220, 2056, -19544, 213216, -2571552, 34036224, -489916416, 7614555648, -127028029440, 2262903109632, -42857715985920, 859647858427392, -18200106158320128, 405498290896693248, -9482120962982547456, 232156555727228971008

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..444

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

Formula

a(n) = Sum_{m=1..n} (Sum_{k=m..n} (k!*binomial(m,k-m)*2^(k-m)*Stirling1(n,k))/m!), n > 0, a(0) = 1.

Maple

S:= series(exp(log(1+x)+2*log(1+x)^2), x, 31):
seq(coeff(S, x, j)*j!, j=0..30); # Robert Israel, Jan 30 2018

Mathematica

With[{nn=20}, CoefficientList[Series[Exp[Log[1+x]+2Log[1+x]^2], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 27 2014 *)

Prog

(Maxima)
a(n):=sum(sum(k!*binomial(m, k-m)*2^(k-m)*stirling1(n, k), k, m, n)/m!, m, 1, n);

Crossrefs

Sequence in context: A138546 A019217 A221757 * A009371 A248952 A101502

Adjacent sequences: A189421 A189422 A189423 * A189425 A189426 A189427

Keyword

sign

Author

Vladimir Kruchinin, Apr 21 2011

Status

approved