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A023009
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Number of partitions of n into parts of 10 kinds.
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3
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1, 10, 65, 330, 1430, 5512, 19415, 63570, 195910, 573430, 1605340, 4322110, 11240645, 28341730, 69488650, 166096270, 387890625, 886698670, 1987322415, 4373271870, 9461022285, 20144164040, 42254620785, 87398226990, 178396331100, 359618772656, 716409453320
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: Product_{m>=1} 1/(1-x^m)^10.
a(n) ~ 5^(11/4) * exp(2 * Pi * sqrt(5*n/3)) / (64 * 3^(11/4) * n^(13/4)). - Vaclav Kotesovec, Feb 28 2015
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MAPLE
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with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*10, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008
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MATHEMATICA
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nmax=50; CoefficientList[Series[Product[1/(1-x^k)^10, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 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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