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A265096
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a(n) = Sum_{k=0..n} p(k)*q(k), where p(k) = partition numbers (A000041) and q(k) = partition numbers into distinct parts (A000009).
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0
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1, 2, 4, 10, 20, 41, 85, 160, 292, 532, 952, 1624, 2779, 4597, 7567, 12319, 19711, 30997, 48707, 75167, 115295, 175487, 264665, 395185, 587335, 865371, 1267311, 1845231, 2670627, 3839267, 5498051, 7824331, 11080441, 15624505, 21927225, 30633780, 42642416
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ (sqrt(2)-1) * exp((1+sqrt(2))*Pi*sqrt(n/3)) / (8*3^(1/4)*Pi*n^(5/4)).
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MATHEMATICA
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Table[Sum[PartitionsQ[k]*PartitionsP[k], {k, 0, n}], {n, 0, 50}]
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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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