A293370 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.

1602, 36744, 512787, 5413842, 49654380, 405769740, 3112631737, 22474141722, 156807714204, 1057029675170, 6981434207532, 45160469355996, 288451275981963, 1818548589385302, 11371801475805417, 70522341255530382, 434990774484893184, 2668650839230709592

Offset: 6

Author

Alois P. Heinz, Oct 07 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..1000

Crossrefs

Column k=6 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))(6):
seq(a(n), n=6..30);

Formula

a(n) ~ c * 6^n, where c = 3.760725122262068858184072984846959348360490081749654779894152320389687335... - Vaclav Kotesovec, Oct 11 2017