A294466 Binomial transform of A053529.

1, 2, 7, 34, 221, 1666, 15187, 153602, 1770169, 22379266, 312164831, 4685997922, 76668261397, 1335425319554, 24921410400811, 493075754663746, 10358312736025457, 228862423291312642, 5335861084579488439, 130235118120543955106, 3333808742649699747661

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..441

Formula

E.g.f.: exp(x)/eta(x), where eta(x) is the Dedekind eta function.

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)).

E.g.f.: exp(x + Sum_{k>=1} sigma(k)*x^k/k). - Ilya Gutkovskiy, Oct 15 2018

Mathematica

Table[Sum[Binomial[n, k]*k!*PartitionsP[k], {k, 0, n}], {n, 0, 20}]
nmax = 20; CoefficientList[Series[Exp[x] * x^(1/24)/DedekindEta[Log[x]/(2*Pi*I)], {x, 0, nmax}], x] * Range[0, nmax]!

Prog

(PARI) x='x+O('x^50); Vec(serlaplace(exp(x)/eta(x))) \\ G. C. Greubel, Oct 15 2018

Crossrefs

Cf. A218481, A281425, A095051.

Cf. A266232, A294467, A293467, A294468.

Sequence in context: A135882 A143740 A049463 * A029894 A110313 A000944

Adjacent sequences: A294463 A294464 A294465 * A294467 A294468 A294469

Keyword

nonn

Author

Vaclav Kotesovec, Oct 31 2017

Status

approved