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A292720
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Number of multisets of nonempty words with a total of n letters over 5-ary alphabet such that within each word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
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2
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1, 1, 4, 14, 67, 343, 1431, 6620, 31539, 151680, 769374, 3586756, 17500630, 85727012, 420986605, 2116435479, 10254063794, 50697425138, 251055167912, 1244053731675, 6246442090103, 30737278735067, 152890117563022, 761050222982081, 3790169351183134
(list;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: Product_{j>=1} 1/(1-x^j)^A226875(j).
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MAPLE
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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, 5), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..35);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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