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

9,2

Links

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

Formula

a(n) ~ 8^(n-1) / (8! * QPochhammer[1/8]). - 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))(9):
seq(a(n), n=9..40);

Crossrefs

Column k=9 of A262495.

Cf. A258464.

Sequence in context: A220684 A225971 A258463 * A211834 A216439 A333065

Adjacent sequences: A320548 A320549 A320550 * A320552 A320553 A320554

Keyword

nonn

Author

Alois P. Heinz, Oct 15 2018

Status

approved