login
A327289
Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size six are used and the colors are introduced in increasing order.
2
1, 2, 5, 10, 20, 36, 65, 123, 210, 362, 603, 994, 1595, 2541, 3956, 6225, 9501, 14516, 21820, 32703, 48315, 71175, 103589, 150167, 216413, 309627, 440400, 623404, 877303, 1228493, 1712235, 2374639, 3278894, 4507571, 6175713, 8421243, 11447049, 15496728
OFFSET
21,2
LINKS
FORMULA
a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-5))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-5)) / (4*6!*sqrt(18)*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!)(6):
seq(a(n), n=21..59);
CROSSREFS
Column k=6 of A321878.
Sequence in context: A327291 A327290 A227356 * A327288 A102688 A236559
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 28 2019
STATUS
approved