This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A369888 #10 Feb 04 2024 09:01:46 %S A369888 1,1,9,36,108,449,1212,4499,10914,43286,103296,306994,867763,2165484, %T A369888 6627800,16827227,42203212,104397436,282967414,632194758,1809241372, %U A369888 4120266946,10256452121,23140530512,55030272918,130803096050,291295024121,739011803928,1634625423738 %N A369888 Sum of products of cubes of parts , counted without multiplicity, in all partitions of n. %F A369888 G.f.: Product_{k>=1} 1 + k^3*x^k/(1-x^k). %e A369888 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. %o A369888 (PARI) my(N=30, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^3*x^k/(1-x^k))) %Y A369888 Cf. A162506, A369887. %Y A369888 Cf. A265837. %K A369888 nonn %O A369888 0,3 %A A369888 _Seiichi Manyama_, Feb 04 2024