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

1,3

Links

Table of n, a(n) for n=1..19.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A199359 A199584 A087675 * A299529 A014632 A117985

Adjacent sequences: A128041 A128042 A128043 * A128045 A128046 A128047

Keyword

nonn,frac

Author

Leroy Quet, Feb 11 2007

Extensions

Extended by Ray Chandler, Feb 12 2007

Status

approved