A128044 a(n) = numerator of b(n), where b(1) = 1, b(n) = Sum_{k=1..n-1} b(n-k) * H(k); H(k) = Sum_{j=1..k} 1/j, the k-th harmonic number.

1, 1, 5, 35, 27, 156, 25951, 419681, 646379, 13439609, 5544403, 56359019, 109370096651, 218981057573, 1073115579569, 334684898286103, 8505202310547841, 515483074900523, 712333151156230489

Offset: 1

Author

Leroy Quet, Feb 11 2007

Keywords

• nonn
• frac

Examples

			1, 1, 5/2, 35/6, 27/2, 156/5, 25951/360, 419681/2520, 646379/1680, 13439609/15120, 5544403/2700, 56359019/11880, ...
		

Crossrefs

Cf. A001008, A002805, A128045 (denominators), A305306.

Programs

Mathematica

f[l_List] := Block[{n = Length[l] + 1},Append[l, Sum[l[[n - k]]*HarmonicNumber[k], {k, n - 1}]]];Numerator[Nest[f, {1}, 20]] (* Ray Chandler, Feb 12 2007 *)

Formula

G.f. for fractions: x / (1 + log(1 - x) / (1 - x)). - Ilya Gutkovskiy, Sep 01 2021

Extensions

Extended by Ray Chandler, Feb 12 2007