%I
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,4,2,4,4,5,4,7,5,7,7,8,7,10,8,
%U 10,10,11,10,15,12,14,15,17,15,19,17,20,20,21,20,25,22,24,25,27,25,32,28,32,32,34,34,39,35,39,40,43,40,46,43,47
%N Number of partitions of n where every part appears at least 18 times
%H R. H. Hardin, <a href="/A160988/b160988.txt">Table of n, a(n) for n=1..1000</a>
%F a(n) ~ sqrt(Pi^2 + 6*c) * exp(sqrt((2*Pi^2/3 + 4*c)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1  exp(x) + exp(18*x)) dx = 1.334989118601880353022790449460912585887590533324376464199... .  _Vaclav Kotesovec_, Jan 05 2016
%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(18*k)/(1x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)
%K nonn
%O 1,36
%A _R. H. Hardin_ Jun 01 2009
