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%I #12 Nov 20 2017 05:33:22
%S 0,0,0,1,1,2,3,5,7,10,14,20,26,36,47,62,80,104,132,169,212,267,332,
%T 414,510,629,769,941,1142,1386,1672,2016,2417,2897,3455,4118,4888,
%U 5796,6849,8085,9513,11182,13107,15347,17923,20910,24338,28298,32833,38054,44021
%N Number of partitions of n having exactly one part that is a multiple of 3.
%C Column 1 of A116633.
%H G. C. Greubel, <a href="/A116634/b116634.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: x^3/((1-x^3)*Product_{j>=1} ((1-x^(3j-2))(1-x^(3j-1))).
%F a(n) ~ exp(2*Pi*sqrt(n)/3) / (6*Pi*n^(1/4)). - _Vaclav Kotesovec_, Mar 07 2016
%e a(7)=5 because we have [6,1],[4,3],[3,2,2],[3,2,1,1] and [3,1,1,1,1].
%p g:=x^3/(1-x^3)/product((1-x^(3*j-2))*(1-x^(3*j-1)),j=1..30): gser:=series(g,x=0,56): seq(coeff(gser,x,n),n=0..53);
%t nmax = 50; CoefficientList[Series[x^3/(1-x^3) * Product[1/((1-x^(3*k-2))*(1-x^(3*k-1))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 07 2016 *)
%Y Cf. A116633, A000726.
%K nonn
%O 0,6
%A _Emeric Deutsch_, Feb 19 2006
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