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Number of partitions of n where every part appears at least 14 times
1

%I #8 Jan 05 2016 12:07:11

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,

%T 1,2,1,2,1,2,1,4,2,4,4,5,4,7,5,7,7,8,7,10,8,12,11,12,12,16,13,16,16,

%U 18,17,20,18,22,21,25,23,28,25,29,30,32,30,35,33,38,36,39,38,47,43,48,48,54,52,63,58,67,65,74,73,85,79,95

%N Number of partitions of n where every part appears at least 14 times

%H R. H. Hardin, <a href="/A160984/b160984.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(-14*x)) dx = -1.284573189673851723704615507462186169038822303924896813445... . - _Vaclav Kotesovec_, Jan 05 2016

%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(14*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)

%K nonn

%O 1,28

%A _R. H. Hardin_ Jun 01 2009