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A270105
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a(n) = Sum_{k=0..n} k*A000009(k).
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0
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0, 1, 3, 9, 17, 32, 56, 91, 139, 211, 311, 443, 623, 857, 1165, 1570, 2082, 2728, 3556, 4582, 5862, 7458, 9416, 11808, 14736, 18286, 22576, 27760, 33976, 41400, 50280, 60820, 73300, 88084, 105492, 125967, 150015, 178135, 210967, 249265, 293785, 345445, 405337
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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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a(n) ~ 3^(1/4) * n^(3/4) * exp(sqrt(n/3)*Pi) / (2*Pi).
G.f.: x*f'(x)/(1 - x), where f(x) = Product_{k>=1} (1 + x^k). - Ilya Gutkovskiy, Apr 13 2017
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MATHEMATICA
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Table[Sum[PartitionsQ[k]*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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