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A293971
Number of sets of exactly nine 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
45, 740, 7265, 54844, 355786, 2086218, 11402599, 59244154, 296592681, 1444795518, 6898985716, 32478508414, 151439118998, 702039301562, 3246061184641, 15011635714770, 69604533115983, 324297338323040, 1521325113273431, 7199243859471728, 34426802099939524
OFFSET
25,1
LINKS
FORMULA
a(n) = [x^n y^9] 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, 10)
end:
a:= n-> coeff(b(n$2), x, 9):
seq(a(n), n=25..49);
CROSSREFS
Column k=9 of A293815.
Cf. A000085.
Sequence in context: A105251 A099632 A264138 * A341427 A024379 A134290
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2017
STATUS
approved