A128045 - OEIS

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.

%I #13 Sep 01 2021 22:21:32

%S 1,1,2,6,2,5,360,2520,1680,15120,2700,11880,9979200,8648640,18345600,

%T 2476656000,27243216000,714714000,427508928000,1160381376000,

%U 1055947052160000,22174888095360000,38718058579200,141031842336000

%N 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.

%F G.f. for fractions: x / (1 + log(1 - x) / (1 - x)). - _Ilya Gutkovskiy_, Sep 01 2021

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

%t 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 *)

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

%K nonn,frac

%O 1,3

%A _Leroy Quet_, Feb 11 2007

%E Extended by _Ray Chandler_, Feb 12 2007