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.

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

Alois P. Heinz, Table of n, a(n) for n = 28..5000

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

Adjacent sequences: A327287 A327288 A327289 * A327291 A327292 A327293

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2019

Status

approved