A320344 Expansion of e.g.f. log(1 + x)/(1 - log(1 + x))^2.

0, 1, 3, 8, 26, 94, 406, 1896, 10440, 59472, 405264, 2673648, 22396128, 160828368, 1704287568, 11993279232, 177349981824, 957018589056, 25766036316288, 33555346603776, 5403108443855616, -28811285794990080, 1643455634670489600, -21001090458387594240, 692074413969784289280

Offset: 0

Author

Ilya Gutkovskiy, Jan 22 2019

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..451

Crossrefs

Cf. A001563, A048994, A069321, A215916, A317280, A351280.

Programs

Maple

seq(n!*coeff(series(log(1+x)/(1-log(1+x))^2,x=0,25),x,n),n=0..24); # Paolo P. Lava, Jan 29 2019

Mathematica

nmax = 24; CoefficientList[Series[Log[1 + x]/(1 - Log[1 + x])^2, {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k k!, {k, 0, n}], {n, 0, 24}]

PARI

my(N=40, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, N, k*log(1+x)^k)))) \\ Seiichi Manyama, Apr 22 2022

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A001563(k).

E.g.f.: Sum_{k>=0} k * log(1+x)^k. - Seiichi Manyama, Apr 22 2022