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%I #8 Jan 05 2016 12:06:21
%S 0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,1,2,
%T 1,4,2,4,4,5,4,7,5,7,7,8,7,12,9,11,12,14,12,16,14,17,17,18,17,25,20,
%U 23,24,27,26,30,27,32,32,34,32,43,37,42,44,49,47,57,52,63,61,68,66,86,77,88,89,103,98,118,112,130
%N Number of partitions of n where every part appears at least 12 times
%H R. H. Hardin, <a href="/A160982/b160982.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(-12*x)) dx = -1.250113645567074508329122746243739037481172772185350892378... . - _Vaclav Kotesovec_, Jan 05 2016
%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(12*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)
%K nonn
%O 1,24
%A _R. H. Hardin_ Jun 01 2009
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