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A340411
Number of sets of nonempty words with a total of n letters over quaternary 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, 206, 865, 3408, 15025, 57175, 240741, 961035, 4132903, 16279273, 68134510, 274714351, 1164578487, 4657730815, 19404869767, 78676610521, 330495175277, 1332463920931, 5531856232294, 22498784991153, 93925698566719, 380437352382876
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{j>=1} (1+x^j)^A092429(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, 4)):
seq(a(n), n=0..32);
CROSSREFS
Column k=4 of A292795.
Cf. A092429.
Sequence in context: A317776 A145942 A331517 * A074437 A026578 A362596
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 06 2021
STATUS
approved