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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. 2
120, 2010, 21082, 169846, 1173098, 7286181, 41993502, 228997683, 1198101638, 6074435686, 30073235682, 146248264684, 701957684114, 3338454463793, 15784582285468, 74407037119692, 350575594435412, 1654700449779204, 7840223330719670, 37363522942015498 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 26 11:22 EST 2022. Contains 350598 sequences. (Running on oeis4.)