A320552 Number of partitions of n into parts of exactly ten sorts which are introduced in ascending order such that sorts of adjacent parts are different.

1, 46, 1202, 23523, 384227, 5542879, 73055550, 899381476, 10501235760, 117575627562, 1272685923725, 13401470756234, 137945728220808, 1393299928219652, 13851195993229478, 135865787060384468, 1317624915100586227, 12654868264707472392, 120534359759023933905

Offset

10,2

Links

Alois P. Heinz, Table of n, a(n) for n = 10..1000

Formula

a(n) ~ 9^(n-1) / (9! * QPochhammer[1/9]). - Vaclav Kotesovec, Oct 25 2018

Maple

b:= proc(n, i, k) option remember; `if`(n=0 or i=1, k^(n-1),
      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k)))
    end:
A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, k*b(n$2, k-1))):
a:= n-> (k-> add(A(n, k-i)*(-1)^i/(i!*(k-i)!), i=0..k))(10):
seq(a(n), n=10..40);

Crossrefs

Column k=10 of A262495.

Cf. A258465.

Sequence in context: A004424 A361183 A258464 * A211835 A333066 A261940

Adjacent sequences: A320549 A320550 A320551 * A320553 A320554 A320555

Keyword

nonn

Author

Alois P. Heinz, Oct 15 2018

Status

approved