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%I #29 Oct 15 2018 22:19:34
%S 1,0,3,8,69,384,4375,34152,464457,5051456,75865131,1032865800,
%T 18108977293,286975230528,5639956035519,105513165321704,
%U 2269311347406225,48066460265622912,1146324511845384787,26924271371612501256,701472699537610875861,18214089447110112972800,512194770431254272442983
%N E.g.f.: exp(-x)/eta(x), where eta(x) is the Dedekind eta function.
%H Vaclav Kotesovec, <a href="/A095051/b095051.txt">Table of n, a(n) for n = 0..440</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Inverse binomial transform of A053529. - _Vladeta Jovovic_, Jun 21 2004
%F From _Vaclav Kotesovec_, Oct 31 2017: (Start)
%F a(n) ~ exp(-1) * n! * A000041(n).
%F a(n) ~ sqrt(2*Pi) * exp(Pi*sqrt(2*n/3) - n - 1) * n^(n - 1/2) / (4*sqrt(3)). (End)
%F E.g.f.: exp(Sum_{k>=2} sigma(k)*x^k/k). - _Ilya Gutkovskiy_, Oct 15 2018
%t Table[Sum[(-1)^(n-k) * Binomial[n, k] * k! * PartitionsP[k], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Oct 31 2017 *)
%t nmax = 20; CoefficientList[Series[Exp[-x] * x^(1/24)/DedekindEta[Log[x]/(2*Pi*I)], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 31 2017 *)
%o (PARI) a(n)=polcoeff(1/eta(x)/exp(x),n)*n!
%Y Cf. A218481, A294466, A281425.
%Y Cf. A266232, A294467, A293467, A294468.
%K nonn
%O 0,3
%A _Benoit Cloitre_, Jun 19 2004
%E More terms from _Michel Marcus_, Oct 31 2017
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