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A293366
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Number of partitions of n where each part i is marked with a word of length i over a binary alphabet whose letters appear in alphabetical order and both letters occur at least once in the partition.
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3
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3, 12, 40, 104, 279, 654, 1577, 3560, 8109, 17734, 39205, 83996, 181043, 382856, 811084, 1694468, 3545864, 7340308, 15205768, 31259422, 64253260, 131314502, 268332975, 545854344, 1110087515, 2250051262, 4558868119, 9213241988, 18613362500, 37529700206
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OFFSET
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2,1
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))
end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(2):
seq(a(n), n=2..35);
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + If[i > n, 0, b[n - i, i, k] Binomial[i + k - 1, k - 1]]]];
a[n_] := With[{k = 2}, Sum[b[n, n, k - i] (-1)^i Binomial[k, i], {i, 0, k}]];
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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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