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 A369887 Sum of products of squares of parts , counted without multiplicity, in all partitions of n. 1
 1, 1, 5, 14, 34, 95, 208, 537, 1090, 2812, 5566, 12480, 26199, 53486, 112866, 229111, 450800, 885030, 1778190, 3319846, 6624376, 12354288, 23674929, 43485580, 81441398, 149864634, 273431081, 503205344, 906757150, 1630802024, 2920280596, 5166820832 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..31. FORMULA G.f.: Product_{k>=1} 1 + k^2*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) = 16 + 9 + 4 + 4 + 1 = 34. PROG (PARI) my(N=40, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^2*x^k/(1-x^k))) CROSSREFS Cf. A162506, A369888. Cf. A077335. Sequence in context: A094584 A023515 A047860 * A083332 A101015 A076858 Adjacent sequences: A369884 A369885 A369886 * A369888 A369889 A369890 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 04 2024 STATUS approved

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Last modified April 20 07:43 EDT 2024. Contains 371799 sequences. (Running on oeis4.)