A107236 - OEIS

%I #12 Jan 07 2021 09:53:08

%S 1,1,1,2,3,3,5,6,8,11,13,16,22,26,32,40,49,59,73,87,105,126,151,178,

%T 214,252,297,351,413,481,566,658,767,892,1034,1195,1386,1595,1838,

%U 2114,2429,2781,3189,3642,4160,4744,5404,6141,6986,7921,8980

%N Expansion of 1 / Product_{n>=0} (1 - q^(5n+1))*(1 - q^(5n+3))*(1 - q^(5n+4)).

%H Vaclav Kotesovec, <a href="/A107236/b107236.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ Pi^(3/5) * exp(Pi*sqrt(2*n/5)) / (Gamma(2/5) * 2^(4/5) * 5^(7/10) * n^(4/5)). - _Vaclav Kotesovec_, Jan 07 2021

%t nmax = 50; CoefficientList[Series[1/Product[(1 - x^(5*k+1))*(1 - x^(5*k+3))*(1 - x^(5*k+4)), {k, 0, nmax/5}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jan 07 2021 *)

%Y Cf. A035959, A107234, A107235, A107237.

%K nonn

%O 0,4

%A _Ralf Stephan_, May 13 2005