A327292 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size nine are used and the colors are introduced in increasing order.

1, 2, 5, 10, 20, 36, 65, 110, 185, 300, 515, 819, 1332, 2102, 3327, 5142, 7958, 12071, 18271, 27256, 40462, 60036, 87981, 128502, 186484, 269466, 386757, 553271, 786299, 1113510, 1568109, 2199730, 3069546, 4278447, 5924730, 8188867, 11266659, 15464516, 21134748

Offset

45,2

Links

Alois P. Heinz, Table of n, a(n) for n = 45..5000

Formula

a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-8))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-8)) / (4*9!*sqrt(27)*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!)(9):
seq(a(n), n=45..83);

Crossrefs

Column k=9 of A321878.

Sequence in context: A000712 A032442 A327293 * A327291 A327290 A227356

Adjacent sequences: A327289 A327290 A327291 * A327293 A327294 A327295

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2019

Status

approved