A302547 Expansion of e.g.f. -log(1 - log(1 + x))/(1 - log(1 + x)).

0, 1, 2, 4, 11, 33, 131, 516, 2810, 12934, 97870, 447940, 5308112, 16394116, 450505844, -315178912, 60774618672, -394330113648, 12662225550288, -157622647720032, 3766647294946944, -64679214198647520, 1475157821754785184, -30431206030329719424, 719032203373502252160

Offset: 0

Author

Ilya Gutkovskiy, Jun 20 2018

Keywords

• sign

Examples

			E.g.f.: A(x) = x + 2*x^2/2! + 4*x^3/3! + 11*x^4/4! + 33*x^5/5! + 131*x^6/6! + ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..451

Crossrefs

Cf. A000254, A001008, A002805, A006252, A073596, A089064, A222058, A300490, A302548.

Programs

Maple

H:= proc(n) H(n):= 1/n +`if`(n=1, 0, H(n-1)) end:
a:= n-> add(Stirling1(n, k)*H(k)*k!, k=1..n):
seq(a(n), n=0..27);  # Alois P. Heinz, Jun 21 2018

Mathematica

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

Formula

a(n) = Sum_{k=1..n} Stirling1(n,k)*H(k)*k!, where H(k) is the k-th harmonic number.