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A340417
Number of sets of nonempty words with a total of n letters over denary 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, 10339365, 72459687, 581246095, 4483235005, 36697945720, 298344453071, 2601248199787, 22469318990159, 208007606797845, 1867498245975013, 17978675539264085, 153181998023380623, 1392447676785436846
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{j>=1} (1+x^j)^A226880(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, 10)):
seq(a(n), n=0..32);
CROSSREFS
Column k=10 of A292795.
Cf. A226880.
Sequence in context: A340414 A340415 A340416 * A292796 A020007 A112731
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 07 2021
STATUS
approved