A293972 Number of sets of exactly ten nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

120, 2010, 21082, 169846, 1173098, 7286181, 41993502, 228997683, 1198101638, 6074435686, 30073235682, 146248264684, 701957684114, 3338454463793, 15784582285468, 74407037119692, 350575594435412, 1654700449779204, 7840223330719670, 37363522942015498

Offset

29,1

Links

Alois P. Heinz, Table of n, a(n) for n = 29..823

Formula

a(n) = [x^n y^10] Product_{j>=1} (1+y*x^j)^A000085(j).

Maple

g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 11)
    end:
a:= n-> coeff(b(n$2), x, 10):
seq(a(n), n=29..53);

Crossrefs

Column k=10 of A293815.

Cf. A000085.

Sequence in context: A346574 A244838 A266343 * A144858 A084030 A056291

Adjacent sequences: A293969 A293970 A293971 * A293973 A293974 A293975

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2017

Status

approved