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A258788 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)).

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%I A258788 #10 Jun 11 2015 06:25:51
%S A258788 1,1,3,12,47,192,811,3539,15765,71362,327748,1524081,7161629,33958506,
%T A258788 162312471,781305581,3784573140,18435578714,90261022638,443956543235,
%U A258788 2192796266004,10872208762458,54095648185434,270029668955605,1351943521270155,6787479872751732
%N A258788 a(n) = [x^n] Product_{k=1..n} 1/(x^k*(1-x^k)).
%H A258788 Vaclav Kotesovec, <a href="/A258788/b258788.txt">Table of n, a(n) for n = 0..494</a>
%F A258788 a(n) ~ c * d^n / n^2, where d = A258234 = 5.40087190411815415246609111910427005202943771019167057093170601448448... = r^2/(r-1), where r is the root of the equation polylog(2, 1-r) + log(r)^2 = 0, c = 2.578341962163260914344332458898614289944... .
%p A258788 T:=proc(n, k) option remember; `if`(n=0 or k=1, 1, T(n, k-1) + `if`(n<k, 0, T(n-k, k))) end proc: seq(T(n*(n+3)/2, n), n=0..30);
%t A258788 Table[SeriesCoefficient[1/Product[x^k*(1-x^k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
%t A258788 Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}], {x, 0, n*(n+3)/2}], {n, 0, 30}]
%Y A258788 Cf. A258234, A258789, A258797.
%K A258788 nonn
%O A258788 0,3
%A A258788 _Vaclav Kotesovec_, Jun 10 2015