A369887 Sum of products of squares of parts , counted without multiplicity, in all partitions of n.
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
Offset: 0
Keywords
Examples
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.
Programs
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PARI
my(N=40, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^2*x^k/(1-x^k)))
Formula
G.f.: Product_{k>=1} 1 + k^2*x^k/(1-x^k).