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A292718
Number of multisets 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, 4, 14, 43, 139, 495, 1544, 5111, 17348, 55520, 181946, 607300, 1951262, 6362769, 20972812, 67451405, 218884282, 715353298, 2298626230, 7429125757, 24124615697, 77400570114, 249285637563, 805472940377, 2579640351769, 8283108375403, 26655874638762
OFFSET
0,3
LINKS
FORMULA
G.f.: Product_{j>=1} 1/(1-x^j)^A092255(j).
Euler transform of A092255.
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:
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*d!*
b(d, 0, 3), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..35);
CROSSREFS
Column k=3 of A292712.
Sequence in context: A247470 A049539 A037528 * A212688 A261451 A084613
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 21 2017
STATUS
approved