A292719 Number of multisets of nonempty words with a total of n letters over quaternary 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, 223, 951, 3680, 16239, 61656, 260490, 1035820, 4451494, 17534372, 73518595, 295928531, 1253898892, 5015867442, 20920480946, 84742519783, 355861723649, 1434993799839, 5962065435072, 24234396539097, 101149561260620, 409761023233915

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)^A092429(j).

Euler transform of A092429.

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

Crossrefs

Column k=4 of A292712.

Cf. A092429, A226873.

Sequence in context: A187742 A347432 A129219 * A292720 A292721 A292722

Adjacent sequences: A292716 A292717 A292718 * A292720 A292721 A292722

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2017

Status

approved