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%I #8 Jan 05 2016 12:08:22
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,
%T 1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,3,3,3,5,4,5,6,6,6,8,7,8,9,9,9,11,10,
%U 13,13,13,14,17,15,17,18,19,19,21,20,23,23,23,24,27,28,28,30,31,32,35,34,36,38,38,40,42,42,43,45,47,47,53,51
%N Number of partitions of n where every part appears at least 17 times
%H R. H. Hardin, <a href="/A160987/b160987.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(-17*x)) dx = -1.324115652777071770633973742770277572729211213136860871177... . - _Vaclav Kotesovec_, Jan 05 2016
%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(17*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)
%K nonn
%O 1,34
%A _R. H. Hardin_ Jun 01 2009
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