A320551 Number of partitions of n into parts of exactly nine sorts which are introduced in ascending order such that sorts of adjacent parts are different.

1, 37, 788, 12705, 172520, 2084836, 23169639, 241881526, 2406802476, 23064505722, 214505275666, 1947297442708, 17332491414655, 151788374232332, 1311496639251360, 11205023121317869, 94832831557101194, 796244028802170279, 6640545376656272033

Offset: 9

Author

Alois P. Heinz, Oct 15 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..1000

Crossrefs

Column k=9 of A262495.

Cf. A258464.

Programs

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))(9):
seq(a(n), n=9..40);

Formula

a(n) ~ 8^(n-1) / (8! * QPochhammer[1/8]). - Vaclav Kotesovec, Oct 25 2018