A293373 Number of partitions of n where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order and all nine letters occur at least once in the partition.

871030, 41488902, 1106315145, 22148014950, 366764207877, 5369282570448, 71433531608103, 887892874465104, 10433233718235522, 117558189248146187, 1278057588056171991, 13515236446777067727, 139538852470920866367, 1413457490580676488090, 14081562892529164704060

Offset: 9

Author

Alois P. Heinz, Oct 07 2017

Keywords

• nonn

Links

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

Crossrefs

Column k=9 of A261719.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))
    end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(9):
seq(a(n), n=9..30);

Formula

a(n) ~ c * 9^n, where c = 3.23950351986835655716873222462341048089067679826... - Vaclav Kotesovec, Oct 11 2017