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A340409
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Number of sets of nonempty words with a total of n letters over binary 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, 3, 7, 18, 42, 110, 250, 627, 1439, 3523, 8063, 19374, 44274, 104816, 238976, 559171, 1271295, 2946901, 6679741, 15363719, 34719631, 79335385, 178749829, 406164359, 912475815, 2063298409, 4622461673, 10407679805, 23254807241, 52160338735, 116252939071
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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+x^j)^A027306(j).
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EXAMPLE
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a(3) = 7: {aaa}, {aab}, {aba}, {baa}, {aa,a}, {ab,a}, {ba,a}.
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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:
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, 2)):
seq(a(n), n=0..32);
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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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