

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
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OFFSET

0,3


LINKS



FORMULA

G.f.: Product_{k>=1} 1 + k^3*x^k/(1x^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/(1x^k)))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



