A265837 Expansion of Product_{k>=1} 1/(1 - k^3*x^k).

1, 1, 9, 36, 164, 505, 2474, 7273, 31008, 103644, 379890, 1226802, 4747529, 14553648, 52167558, 171639695, 583371802, 1851395692, 6427705062, 19983302144, 67235043192, 214615427776, 697704303005, 2194982897304, 7262755260410, 22402942281766, 72461661415093

Offset: 0

Author

Vaclav Kotesovec, Dec 16 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A006906, A077335, A265838, A265839, A265840.

Column k=3 of A292193.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[1/(1 - k^3*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

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

c = 86.60286320343345379122228784466307940393110978... if n mod 3 = 0

c = 86.27536745612304663727011387030370600864018892... if n mod 3 = 1

c = 86.29819842537784019895326532818285333403267092... if n mod 3 = 2.

G.f.: exp(Sum_{k>=1} Sum_{j>=1} j^(3*k)*x^(j*k)/k). - Ilya Gutkovskiy, Jun 14 2018