A369888 Sum of products of cubes of parts , counted without multiplicity, in all partitions of n.
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
Offset: 0
Keywords
Examples
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.
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^3*x^k/(1-x^k)))
Formula
G.f.: Product_{k>=1} 1 + k^3*x^k/(1-x^k).