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A327384
Number of colored integer partitions of n such that six colors are used and parts differ by size or by color.
6
1, 6, 27, 92, 273, 720, 1751, 3978, 8565, 17618, 34878, 66792, 124268, 225384, 399618, 694294, 1184340, 1986900, 3282991, 5349372, 8604978, 13678190, 21503439, 33459222, 51563824, 78751470, 119259576, 179169140, 267154842, 395521482, 581629358, 849846186
OFFSET
6,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 6..10000 (terms 6..5000 from Alois P. Heinz)
FORMULA
a(n) ~ exp(Pi*sqrt(2*n)) / (2^(17/4) * n^(3/4)). - Vaclav Kotesovec, Sep 16 2019
G.f.: (-1 + Product_{k>=1} (1 + x^k))^6. - Ilya Gutkovskiy, Jan 31 2021
MAPLE
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))(6):
seq(a(n), n=6..45);
MATHEMATICA
A327384[n_] := SeriesCoefficient[(Product[(1 + x^k), {k, 1, n}] - 1)^6, {x, 0, n}]; Table[A327384[n], {n, 6, 37}] (* Robert P. P. McKone, Jan 31 2021 *)
CROSSREFS
Column k=6 of A308680.
Sequence in context: A100189 A052267 A038166 * A121596 A264026 A341385
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 03 2019
STATUS
approved