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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.
2
1, 1, 5, 35, 27, 156, 25951, 419681, 646379, 13439609, 5544403, 56359019, 109370096651, 218981057573, 1073115579569, 334684898286103, 8505202310547841, 515483074900523, 712333151156230489
OFFSET
1,3
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: A199584 A087675 A376610 * A299529 A014632 A117985
KEYWORD
nonn,frac
AUTHOR
Leroy Quet, Feb 11 2007
EXTENSIONS
Extended by Ray Chandler, Feb 12 2007
STATUS
approved