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A160982
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Number of partitions of n where every part appears at least 12 times
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1
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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, 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, 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
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OFFSET
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1,24
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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(-12*x)) dx = -1.250113645567074508329122746243739037481172772185350892378... . - Vaclav Kotesovec, Jan 05 2016
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MATHEMATICA
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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 *)
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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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