cp's OEIS Frontend

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.

A022732 Expansion of Product_{m>=1} 1/(1 - m*q^m)^8.

This page as a plain text file.
%I A022732 #12 Sep 08 2022 08:44:46
%S A022732 1,8,52,272,1274,5408,21448,80080,285043,972496,3200644,10199456,
%T A022732 31592350,95366176,281269560,812094448,2299480441,6394796832,
%U A022732 17489643664,47096042032,124993380566,327249781952
%N A022732 Expansion of Product_{m>=1} 1/(1 - m*q^m)^8.
%H A022732 G. C. Greubel, <a href="/A022732/b022732.txt">Table of n, a(n) for n = 0..1000</a>
%F A022732 G.f.: exp(8*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 07 2018
%t A022732 With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-8, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Jul 25 2018 *)
%o A022732 (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^-8)) \\ _G. C. Greubel_, Jul 25 2018
%o A022732 (Magma) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^8:m in [1..n]])); // _G. C. Greubel_, Jul 25 2018
%Y A022732 Column k=8 of A297328.
%K A022732 nonn
%O A022732 0,2
%A A022732 _N. J. A. Sloane_