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A340412
Number of sets of nonempty words with a total of n letters over quinary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
2
1, 1, 3, 13, 60, 326, 1345, 6228, 29845, 143899, 732765, 3412167, 16623175, 81624325, 400892932, 2018593583, 9773821243, 48292202375, 239383150209, 1186254809797, 5960931333905, 29322695430795, 145800954979162, 726137079681765, 3616351096084351
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{j>=1} (1+x^j)^A226875(j).
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:
g:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), n!*b(n, 0, k)):
h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(h(n-i*j, i-1, k)*binomial(g(i, k), j), j=0..n/i)))
end:
a:= n-> h(n$2, min(n, 5)):
seq(a(n), n=0..32);
CROSSREFS
Column k=5 of A292795.
Cf. A226875.
Sequence in context: A357151 A367058 A353208 * A340413 A340414 A340415
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 06 2021
STATUS
approved