A327293 Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size ten are used and the colors are introduced in increasing order.

1, 2, 5, 10, 20, 36, 65, 110, 185, 300, 481, 795, 1250, 1982, 3087, 4798, 7332, 11191, 16821, 25196, 37308, 54951, 80131, 117346, 169306, 244417, 349967, 500258, 709715, 1005550, 1414751, 1986544, 2773496, 3861747, 5349095, 7389698, 10178856, 13964050, 19102030

Offset

55,2

Comments

In general, for k>=1, is column k of A321878 asymptotic to exp(sqrt(2*(Pi^2 - 6*polylog(2, 1-k))*n/3)) * sqrt(Pi^2 - 6*polylog(2, 1-k)) / (4*k!*sqrt(3*k)*Pi*n). - Vaclav Kotesovec, Sep 18 2019

Links

Alois P. Heinz, Table of n, a(n) for n = 55..5000

Formula

a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-9))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-9)) / (4*10!*sqrt(30)*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!)(10):
seq(a(n), n=55..93);

Crossrefs

Column k=10 of A321878.

Sequence in context: A121597 A000712 A032442 * A327292 A327291 A327290

Adjacent sequences: A327290 A327291 A327292 * A327294 A327295 A327296

Keyword

nonn

Author

Alois P. Heinz, Aug 28 2019

Status

approved