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A293966
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Number of sets of exactly four 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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4, 22, 116, 482, 1966, 7682, 29845, 115438, 449870, 1770788, 7073065, 28727652, 118907910, 502249944, 2167410896, 9563204836, 43166853057, 199391604156, 942578850020, 4559743209208, 22566589645408, 114215149597312, 590875202641724, 3122678708581528
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OFFSET
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8,1
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LINKS
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FORMULA
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a(n) = [x^n y^4] 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, 5)
end:
a:= n-> coeff(b(n$2), x, 4):
seq(a(n), n=8..33);
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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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