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 A270105 a(n) = Sum_{k=0..n} k*A000009(k). 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA 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 MATHEMATICA Table[Sum[PartitionsQ[k]*k, {k, 0, n}], {n, 0, 50}] CROSSREFS Cf. A000009, A000070, A014153, A036469, A095944, A182738. Partial sums of A066189. Sequence in context: A006459 A349489 A049778 * A294425 A123325 A239206 Adjacent sequences:  A270102 A270103 A270104 * A270106 A270107 A270108 KEYWORD nonn,changed AUTHOR Vaclav Kotesovec, Mar 12 2016 STATUS approved

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Last modified July 7 13:21 EDT 2022. Contains 355148 sequences. (Running on oeis4.)