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A293967
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Number of sets of exactly five nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a 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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6, 48, 274, 1338, 6035, 25874, 108002, 444458, 1818905, 7451418, 30693022, 127604480, 536876960, 2291507552, 9939572897, 43885543586, 197465168488, 906430558822, 4247727231198, 20333276583188, 99450038211268, 497066503157976, 2538584563166367
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OFFSET
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11,1
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LINKS
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FORMULA
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a(n) = [x^n y^5] Product_{j>=1} (1+y*x^j)^A000085(j).
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MAPLE
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g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 6)
end:
a:= n-> coeff(b(n$2), x, 5):
seq(a(n), n=11..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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