A292712 -id:A292712 - cp's OEIS frontend

A292724 Number of multisets of nonempty words with a total of n letters over 9-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, 6837054, 49975756, 358031350, 2673108092, 20399335633, 161247005007, 1321885836686, 10814140769210, 93349395210404, 726371063425227, 5939975798740967, 48195816632614079, 396235068140514442

Offset: 0

Alois P. Heinz, Sep 21 2017

nonn

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

Column k=9 of A292712.

Cf. A226879, A226873.

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

G.f.: Product_{j>=1} 1/(1-x^j)^A226879(j).

Euler transform of A226879.

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.

Original entry on oeis.org

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

Alois P. Heinz, Sep 21 2017

nonn

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

Column k=10 of A292712.

Cf. A226880, A226873.

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);

G.f.: Product_{j>=1} 1/(1-x^j)^A226880(j).

Euler transform of A226880.

cp's OEIS Frontend

A292724 Number of multisets of nonempty words with a total of n letters over 9-ary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

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