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 A369888 Sum of products of cubes of parts , counted without multiplicity, in all partitions of n. 1
 1, 1, 9, 36, 108, 449, 1212, 4499, 10914, 43286, 103296, 306994, 867763, 2165484, 6627800, 16827227, 42203212, 104397436, 282967414, 632194758, 1809241372, 4120266946, 10256452121, 23140530512, 55030272918, 130803096050, 291295024121, 739011803928, 1634625423738 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..28. FORMULA G.f.: Product_{k>=1} 1 + k^3*x^k/(1-x^k). EXAMPLE The partitions of 4 are 4, 3+1, 2+2, 2+1+1, 1+1+1+1. So a(4) = 64 + 27 + 8 + 8 + 1 = 108. PROG (PARI) my(N=30, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^3*x^k/(1-x^k))) CROSSREFS Cf. A162506, A369887. Cf. A265837. Sequence in context: A298442 A212104 A193007 * A259279 A168569 A213283 Adjacent sequences: A369885 A369886 A369887 * A369889 A369890 A369891 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 04 2024 STATUS approved

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Last modified May 26 16:22 EDT 2024. Contains 372840 sequences. (Running on oeis4.)