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A095051 E.g.f.: exp(-x)/eta(x), where eta(x) is the Dedekind eta function. 8
1, 0, 3, 8, 69, 384, 4375, 34152, 464457, 5051456, 75865131, 1032865800, 18108977293, 286975230528, 5639956035519, 105513165321704, 2269311347406225, 48066460265622912, 1146324511845384787, 26924271371612501256, 701472699537610875861, 18214089447110112972800, 512194770431254272442983 (list; graph; refs; listen; history; text; internal format)
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: A224230 A053740 A134173 * A092372 A208817 A060752

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

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Last modified September 28 01:20 EDT 2020. Contains 337388 sequences. (Running on oeis4.)