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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
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. A265837.
Sequence in context: A298442 A212104 A193007 * A259279 A168569 A213283
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.)