A292725 Number of multisets of nonempty words with a total of n letters over 10-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, 119259, 1055520, 10465854, 73562956, 592088950, 4560084092, 37322365393, 303133205967, 2640424710926, 22786686453050, 210764523790244, 1891228958070987, 18197644702881767, 155143878113188799, 1411297482751989322

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)^A226880(j).

Euler transform of A226880.

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

Crossrefs

Column k=10 of A292712.

Cf. A226880, A226873.

Sequence in context: A292722 A292723 A292724 * A292713 A007025 A221538

Adjacent sequences: A292722 A292723 A292724 * A292726 A292727 A292728

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2017

Status

approved