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A291693
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Expansion of Product_{k>=1} (1 + x^q(k)), where q(k) = [x^k] Product_{k>=1} (1 + x^k).
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1
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1, 2, 3, 5, 6, 8, 11, 13, 16, 19, 22, 26, 30, 34, 38, 44, 49, 54, 62, 67, 74, 83, 89, 98, 107, 115, 124, 134, 145, 155, 168, 178, 189, 206, 217, 231, 247, 259, 277, 294, 310, 327, 345, 365, 382, 404, 424, 444, 470, 489, 513, 539, 561, 588, 613, 641, 670, 699, 729, 756, 791, 824
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OFFSET
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0,2
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COMMENTS
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Number of partitions of n into distinct terms of A000009, where 2 different parts of 1 and 2 different parts of 2 are available (1a, 1b, 2a, 2b, 3a, 4a, 5a, 6a, ...).
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LINKS
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FORMULA
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G.f.: Product_{k>=1} (1 + x^A000009(k)).
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EXAMPLE
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a(3) = 5 because we have [3a], [2a, 1a], [2a, 1b], [2b, 1a] and [2b, 1b].
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MAPLE
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N:= 20: # to get a(0) .. a(A000009(N))
P:= mul(1+x^k, k=1..N):
R:= mul(1+x^coeff(P, x, n)), n=1..N):
seq(coeff(R, x, n), n=0..coeff(P, x, N)); # Robert Israel, Sep 01 2017
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MATHEMATICA
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nmax = 61; CoefficientList[Series[Product[1 + x^PartitionsQ[k], {k, 1, nmax}], {x, 0, nmax}], x]
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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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