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A340416
Number of sets of nonempty words with a total of n letters over nonary 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, 2065, 14508, 116845, 1039459, 6710565, 48872487, 350817295, 2619846205, 20019859960, 158415989711, 1300359929707, 10644485545679, 91963547963925, 715052566412773, 5842504427274965, 47435773495721103, 390005026265914606, 3225674439739003413
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{j>=1} (1+x^j)^A226879(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, 9)):
seq(a(n), n=0..32);
CROSSREFS
Column k=9 of A292795.
Cf. A226879.
Sequence in context: A340413 A340414 A340415 * A340417 A292796 A020007
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 07 2021
STATUS
approved