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A327290
Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size seven are used and the colors are introduced in increasing order.
2
1, 2, 5, 10, 20, 36, 65, 110, 204, 337, 573, 934, 1527, 2416, 3826, 5907, 9088, 13963, 21070, 31642, 47131, 69707, 102214, 149143, 215754, 310547, 443840, 633139, 895294, 1262971, 1770236, 2473601, 3436809, 4761393, 6561269, 9015761, 12330231, 16812326
OFFSET
28,2
LINKS
FORMULA
a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-6))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-6)) / (4*7!*sqrt(21)*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!)(7):
seq(a(n), n=28..65);
CROSSREFS
Column k=7 of A321878.
Sequence in context: A327293 A327292 A327291 * A227356 A327289 A327288
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 28 2019
STATUS
approved