A265838 Expansion of Product_{k>=1} 1/(1 - k^4*x^k).

1, 1, 17, 98, 610, 2531, 18580, 72453, 449494, 2114440, 10753594, 48572844, 272867295, 1137441506, 5834448870, 27276382027, 129389072144, 576677550870, 2884567552542, 12401875640710, 59474089385344, 270438887909580, 1230979340265033, 5477371267093144

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1550

Formula

a(n) ~ c * 3^(4*n/3), where

c = 27.2472595510480930563087281042486261391960582835336715327... if n mod 3 = 0

c = 26.8841208067599453033952496040472485838861626762931432887... if n mod 3 = 1

c = 26.9277867007233095885556073185206409643421012262073908850... if n mod 3 = 2.

G.f.: exp(Sum_{k>=1} Sum_{j>=1} j^(4*k)*x^(j*k)/k). - Ilya Gutkovskiy, Jun 14 2018

Mathematica

nmax = 40; CoefficientList[Series[Product[1/(1 - k^4*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A006906, A077335, A265837, A265839, A265841.

Column k=4 of A292193.

Sequence in context: A023873 A294590 A294586 * A098997 A257449 A301548

Adjacent sequences: A265835 A265836 A265837 * A265839 A265840 A265841

Keyword

nonn

Author

Vaclav Kotesovec, Dec 16 2015

Status

approved