A265837 - OEIS

%I #14 Sep 07 2023 15:51:54

%S 1,1,9,36,164,505,2474,7273,31008,103644,379890,1226802,4747529,

%T 14553648,52167558,171639695,583371802,1851395692,6427705062,

%U 19983302144,67235043192,214615427776,697704303005,2194982897304,7262755260410,22402942281766,72461661415093

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

%H Vaclav Kotesovec, <a href="/A265837/b265837.txt">Table of n, a(n) for n = 0..2000</a>

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

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

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

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

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

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

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

%Y Column k=3 of A292193.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Dec 16 2015