A293372 Number of partitions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all eight letters occur at least once in the partition.

95503, 3641992, 80387608, 1322729896, 18385756520, 225257353792, 2541255024732, 26777904754008, 269047552566188, 2594409873644384, 24281765931659608, 221357827678662984, 1978440640155108276, 17375505823280757968, 150542570789825846856, 1288702165811231618744

Offset: 8

Author

Alois P. Heinz, Oct 07 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..1000

Crossrefs

Column k=8 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))(8):
seq(a(n), n=8..30);

Formula

a(n) ~ c * 8^n, where c = 3.3565128773700137140303140039343582841894554205106317247... - Vaclav Kotesovec, Oct 11 2017