A292722 Number of multisets of nonempty words with a total of n letters over 7-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, 14900, 78939, 470880, 2805054, 17296396, 110869750, 716116412, 4868928433, 30169477167, 196213489166, 1272224938490, 8371053970724, 55530391931787, 369148740629927, 2514270810574079, 16452249276575722, 109991261928916853

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)^A226877(j).

Euler transform of A226877.

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, 7), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..35);

Crossrefs

Column k=7 of A292712.

Cf. A226877, A226873.

Sequence in context: A292719 A292720 A292721 * A292723 A292724 A292725

Adjacent sequences: A292719 A292720 A292721 * A292723 A292724 A292725

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2017

Status

approved