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A160986
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Number of partitions of n where every part appears at least 16 times
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1
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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, 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, 10, 10, 13, 11, 14, 13, 16, 15, 17, 16, 20, 18, 20, 20, 23, 21, 24, 23, 29, 26, 29, 28, 33, 32, 34, 33, 38, 36, 40, 38, 43, 41, 44, 44, 52, 48, 53, 52, 61, 58
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OFFSET
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1,32
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LINKS
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FORMULA
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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(-16*x)) dx = -1.312209464445062445181826558955439962980138911918364832857... . - Vaclav Kotesovec, Jan 05 2016
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MATHEMATICA
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nmax = 100; Rest[CoefficientList[Series[Product[1 + x^(16*k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 28 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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