A095051 E.g.f.: exp(-x)/eta(x), where eta(x) is the Dedekind eta function.
1, 0, 3, 8, 69, 384, 4375, 34152, 464457, 5051456, 75865131, 1032865800, 18108977293, 286975230528, 5639956035519, 105513165321704, 2269311347406225, 48066460265622912, 1146324511845384787, 26924271371612501256, 701472699537610875861, 18214089447110112972800, 512194770431254272442983
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..440
- N. J. A. Sloane, Transforms
Programs
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Mathematica
Table[Sum[(-1)^(n-k) * Binomial[n, k] * k! * PartitionsP[k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 31 2017 *) 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 *) -
PARI
a(n)=polcoeff(1/eta(x)/exp(x),n)*n!
Formula
Inverse binomial transform of A053529. - Vladeta Jovovic, Jun 21 2004
From Vaclav Kotesovec, Oct 31 2017: (Start)
a(n) ~ exp(-1) * n! * A000041(n).
a(n) ~ sqrt(2*Pi) * exp(Pi*sqrt(2*n/3) - n - 1) * n^(n - 1/2) / (4*sqrt(3)). (End)
E.g.f.: exp(Sum_{k>=2} sigma(k)*x^k/k). - Ilya Gutkovskiy, Oct 15 2018
Extensions
More terms from Michel Marcus, Oct 31 2017