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%I #8 Oct 11 2017 06:43:17
%S 1602,36744,512787,5413842,49654380,405769740,3112631737,22474141722,
%T 156807714204,1057029675170,6981434207532,45160469355996,
%U 288451275981963,1818548589385302,11371801475805417,70522341255530382,434990774484893184,2668650839230709592
%N Number of partitions of n where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order and all six letters occur at least once in the partition.
%H Alois P. Heinz, <a href="/A293370/b293370.txt">Table of n, a(n) for n = 6..1000</a>
%F a(n) ~ c * 6^n, where c = 3.760725122262068858184072984846959348360490081749654779894152320389687335... - _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))(6):
%p seq(a(n), n=6..30);
%Y Column k=6 of A261719.
%K nonn
%O 6,1
%A _Alois P. Heinz_, Oct 07 2017
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