A128045 a(n) = denominator 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, 2, 6, 2, 5, 360, 2520, 1680, 15120, 2700, 11880, 9979200, 8648640, 18345600, 2476656000, 27243216000, 714714000, 427508928000, 1160381376000, 1055947052160000, 22174888095360000, 38718058579200, 141031842336000

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, A128044 (numerators), A305306.

Programs

Mathematica

f[l_List] := Block[{n = Length[l] + 1},Append[l, Sum[l[[n - k]]*HarmonicNumber[k], {k, n - 1}]]];Denominator[Nest[f, {1}, 24]] (* 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