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A327383 Number of colored integer partitions of n such that five colors are used and parts differ by size or by color. 2
1, 5, 20, 60, 160, 381, 845, 1760, 3495, 6660, 12267, 21935, 38230, 65140, 108785, 178437, 287975, 457965, 718575, 1113680, 1706533, 2587655, 3885615, 5781830, 8530625, 12486429, 18140360, 26169335, 37501595, 53403915, 75597130, 106408670, 148973260, 207496090 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 5..10000 (terms 5..5000 from Alois P. Heinz)

Wikipedia, Partition (number theory)

FORMULA

a(n) ~ exp(Pi*sqrt(5*n/3)) * 5^(1/4) / (16 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 16 2019

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))(5):

seq(a(n), n=5..45);

CROSSREFS

Column k=5 of A308680.

Sequence in context: A319888 A319869 A038165 * A215224 A270939 A270631

Adjacent sequences:  A327380 A327381 A327382 * A327384 A327385 A327386

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 03 2019

STATUS

approved

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Last modified September 30 21:27 EDT 2020. Contains 337440 sequences. (Running on oeis4.)