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A327291
Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size eight are used and the colors are introduced in increasing order.
2
1, 2, 5, 10, 20, 36, 65, 110, 185, 326, 532, 879, 1417, 2272, 3563, 5572, 8543, 13031, 19596, 29671, 43971, 65293, 95783, 140259, 203281, 294069, 421433, 602382, 854470, 1207812, 1700895, 2382536, 3323738, 4619166, 6394401, 8817059, 12117260, 16588535, 22637178
OFFSET
36,2
LINKS
FORMULA
a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-7))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-7)) / (4*8!*sqrt(24)*Pi*n). - Vaclav Kotesovec, Sep 18 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))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))
end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(8):
seq(a(n), n=36..75);
CROSSREFS
Column k=8 of A321878.
Sequence in context: A032442 A327293 A327292 * A327290 A227356 A327289
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 28 2019
STATUS
approved