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A340410
Number of sets of nonempty words with a total of n letters over ternary 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, 36, 122, 433, 1356, 4449, 15279, 48567, 158837, 532415, 1704777, 5547148, 18335536, 58815602, 190574866, 623885902, 2000945191, 6459510350, 20998728429, 67275468661, 216477522426, 699952967976, 2239210854373, 7184690267832, 23131348476391
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{j>=1} (1+x^j)^A092255(j).
EXAMPLE
a(3) = 13: {aaa}, {aab}, {aba}, {baa}, {abc}, {acb}, {bac}, {bca}, {cab}, {cba}, {aa,a}, {ab,a}, {ba,a}.
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, 3)):
seq(a(n), n=0..32);
CROSSREFS
Column k=3 of A292795.
Cf. A092255.
Sequence in context: A146424 A146049 A061483 * A128288 A113115 A107136
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 06 2021
STATUS
approved