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A160979 Number of partitions of n where every part appears at least 9 times 1

%I

%S 0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,2,1,2,1,2,1,2,1,2,3,3,3,5,4,5,6,6,

%T 6,10,8,9,11,12,11,14,13,15,19,17,18,22,21,23,25,25,26,33,31,34,37,39,

%U 40,50,46,52,59,62,65,75,74,82,89,98,98,118,115,128,138,147,153,173,174,194,208,220,228,256

%N Number of partitions of n where every part appears at least 9 times

%H R. H. Hardin, <a href="/A160979/b160979.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(-9*x)) dx = -1.177746328175383925002682189470669316299189793135604988217... . - _Vaclav Kotesovec_, Jan 05 2016

%t nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(9*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 28 2015 *)

%K nonn

%O 1,18

%A _R. H. Hardin_ Jun 01 2009

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Last modified September 21 12:21 EDT 2021. Contains 347598 sequences. (Running on oeis4.)