A292721 Number of multisets of nonempty words with a total of n letters over 6-ary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

1, 1, 4, 14, 67, 343, 2151, 9860, 53739, 279360, 1595454, 8733436, 53035750, 280946972, 1626421033, 9103196607, 53266673126, 300953629850, 1817236258604, 10114067087883, 59666856128423, 342703064143223, 2024687556279346, 11644875879288821, 70172335165701018

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{j>=1} 1/(1-x^j)^A226876(j).

Euler transform of A226876.

Maple

b:= proc(n, i, t) option remember; `if`(t=1, 1/n!,
      add(b(n-j, j, t-1)/j!, j=i..n/t))
    end:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*
      b(d, 0, 6), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..35);

Crossrefs

Column k=6 of A292712.

Cf. A226876, A226873.

Sequence in context: A129219 A292719 A292720 * A292722 A292723 A292724

Adjacent sequences: A292718 A292719 A292720 * A292722 A292723 A292724

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2017

Status

approved