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

6,1

Links

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

Formula

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

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);

Crossrefs

Column k=6 of A261719.

Sequence in context: A154505 A031538 A202774 * A352092 A252439 A224949

Adjacent sequences: A293367 A293368 A293369 * A293371 A293372 A293373

Keyword

nonn

Author

Alois P. Heinz, Oct 07 2017

Status

approved