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A327388
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Number of colored integer partitions of n such that ten colors are used and parts differ by size or by color.
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6
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1, 10, 65, 320, 1320, 4762, 15500, 46410, 129710, 341990, 857695, 2059430, 4759235, 10630810, 23034880, 48562378, 99866045, 200766810, 395317950, 763661010, 1449390299, 2706189810, 4976391015, 9021860260, 16139848000, 28515535112, 49792637480, 85989053350
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OFFSET
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10,2
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COMMENTS
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In general, column k > 0 of A308680 is asymptotic to exp(Pi*sqrt(k*n/3)) * k^(1/4) / (3^(1/4) * 2^((k+3)/2) * n^(3/4)). - Vaclav Kotesovec, Sep 16 2019
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LINKS
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FORMULA
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a(n) ~ exp(Pi*sqrt(10*n/3)) * 5^(1/4) / (2^(25/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 16 2019
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add((t->
b(t, min(t, i-1), k)*binomial(k, j))(n-i*j), j=0..min(k, n/i))))
end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(10):
seq(a(n), n=10..45);
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MATHEMATICA
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A327388[n_] := SeriesCoefficient[(Product[(1 + x^k), {k, 1, n}] - 1)^10, {x, 0, n}]; Table[A327388[n], {n, 10, 37}] (* Robert P. P. McKone, Jan 31 2021 *)
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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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