A293372 - OEIS

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.

%I #8 Oct 11 2017 06:44:30

%S 95503,3641992,80387608,1322729896,18385756520,225257353792,

%T 2541255024732,26777904754008,269047552566188,2594409873644384,

%U 24281765931659608,221357827678662984,1978440640155108276,17375505823280757968,150542570789825846856,1288702165811231618744

%N 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.

%H Alois P. Heinz, <a href="/A293372/b293372.txt">Table of n, a(n) for n = 8..1000</a>

%F a(n) ~ c * 8^n, where c = 3.3565128773700137140303140039343582841894554205106317247... - _Vaclav Kotesovec_, Oct 11 2017

%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))

%p end:

%p a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(8):

%p seq(a(n), n=8..30);

%Y Column k=8 of A261719.

%K nonn

%O 8,1

%A _Alois P. Heinz_, Oct 07 2017