A300491 Expansion of e.g.f. log(1 - log(1 - x)/(1 - x)).

0, 1, 2, 4, 9, 28, 140, 936, 6902, 54160, 467784, 4578000, 50434032, 609309504, 7921524624, 110242136928, 1643101763760, 26192405980416, 444523225673472, 7989603260143104, 151483589818925184, 3022296286833907200, 63326051483436129024, 1390571693776506751488

Offset: 0

Author

Ilya Gutkovskiy, Mar 07 2018

Keywords

• nonn

Comments

Logarithmic transform of A000254.

Examples

			log(1 - log(1 - x)/(1 - x)) = x/1! + 2*x^2/2! + 4*x^3/3! + 9*x^4/4! + 28*x^5/5! + 140*x^6/6! + 936*x^7/7! + ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000254, A008405, A087761.

Programs

Maple

b:= proc(n) option remember; `if`(n<2, n, n*b(n-1)+(n-1)!) end:
a:= proc(n) option remember; `if`(n=0, 0, b(n)-add(
      a(j)*j*binomial(n, j)*b(n-j), j=1..n-1)/n)
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 07 2018

Mathematica

nmax = 23; CoefficientList[Series[Log[1 - Log[1 - x]/(1 - x)], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = n! HarmonicNumber[n] - Sum[k Binomial[n, k] (n - k)! HarmonicNumber[n - k] a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 23}]