login
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.
2
1602, 36744, 512787, 5413842, 49654380, 405769740, 3112631737, 22474141722, 156807714204, 1057029675170, 6981434207532, 45160469355996, 288451275981963, 1818548589385302, 11371801475805417, 70522341255530382, 434990774484893184, 2668650839230709592
OFFSET
6,1
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 07 2017
STATUS
approved