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A023007
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Number of partitions of n into parts of 8 kinds.
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5
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1, 8, 44, 192, 726, 2464, 7704, 22528, 62337, 164560, 417140, 1020416, 2418710, 5573568, 12520744, 27484160, 59068372, 124505880, 257770964, 524871424, 1052316364, 2079491744, 4053978040, 7803219968, 14840711765, 27907041392, 51917588800, 95608651776
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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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a(n) ~ exp(4 * Pi * sqrt(n/3)) / (sqrt(2) * 3^(9/4) * n^(11/4)). - 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*8, 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)^8, {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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