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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..440

N. J. A. Sloane, Transforms

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

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 *)

Prog

(PARI) a(n)=polcoeff(1/eta(x)/exp(x), n)*n!

Crossrefs

Cf. A218481, A294466, A281425.

Cf. A266232, A294467, A293467, A294468.

Sequence in context: A053740 A363312 A134173 * A362990 A092372 A208817

Adjacent sequences: A095048 A095049 A095050 * A095052 A095053 A095054

Keyword

nonn

Author

Benoit Cloitre, Jun 19 2004

Extensions

More terms from Michel Marcus, Oct 31 2017

Status

approved