The OEIS is supported by the many generous donors to the OEIS Foundation.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #17 Jan 07 2021 09:52:09
%S 1,1,2,3,4,5,8,10,14,18,23,29,38,47,60,74,92,112,139,168,205,247,298,
%T 356,429,509,607,718,850,1000,1180,1381,1620,1890,2206,2564,2983,3453,
%U 4000,4618,5330,6133,7059,8097,9289,10630,12159,13877
%N Expansion of 1 / Product_{n>=0} (1-q^(5n+1))(1-q^(5n+2))(1-q^(5n+3)).
%C a(n) is the number of partitions of n into parts 5k+1, 5k+2 or 5k+3. - _George Beck_, Aug 09 2020
%H Vaclav Kotesovec, <a href="/A107234/b107234.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) ~ Pi^(1/5) * exp(Pi*sqrt(2*n/5)) / (Gamma(4/5) * 2^(3/5) * 5^(9/10) * n^(3/5)). - _Vaclav Kotesovec_, Jan 07 2021
%t nmax = 50; CoefficientList[Series[1/Product[(1 - x^(5*k+1))*(1 - x^(5*k+2))*(1 - x^(5*k+3)), {k, 0, nmax/5}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jan 07 2021 *)
%Y Cf. A035959, A107235, A107236, A107237.
%K nonn
%O 0,3
%A _Ralf Stephan_, May 13 2005