%I #8 Aug 27 2015 05:57:23

%S 1,1,2,2,2,4,4,5,7,7,9,12,13,16,19,22,26,31,36,41,48,56,63,75,85,96,

%T 112,126,143,165,184,210,238,267,302,340,381,428,480,538,599,672,748,

%U 832,930,1031,1144,1275,1408,1562,1730,1910,2111,2332,2571,2834,3121

%N Number of partitions of n into parts 5k+1 or 5k+3.

%F a(n) ~ exp(2*Pi*sqrt(n/15)) * Gamma(1/5) * Gamma(3/5) / (4 * 3^(3/20) * 5^(7/20) * Pi^(6/5) * n^(13/20)). - _Vaclav Kotesovec_, Aug 27 2015

%t nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(5k+1))*(1 - x^(5k+3))), {k, 0, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Aug 27 2015 *)

%K nonn

%O 1,3

%A _Olivier Gérard_