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

1,3

Links

Table of n, a(n) for n=1..24.

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}]]]; Denominator[Nest[f, {1}, 24]] (* Ray Chandler, Feb 12 2007 *)

Crossrefs

Cf. A001008, A002805, A128044 (numerators), A305306.

Sequence in context: A214775 A196201 A342982 * A011325 A010696 A021796

Adjacent sequences: A128042 A128043 A128044 * A128046 A128047 A128048

Keyword

nonn,frac

Author

Leroy Quet, Feb 11 2007

Extensions

Extended by Ray Chandler, Feb 12 2007

Status

approved