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.

A022731 Expansion of Product_{m>=1} 1/(1 - m*q^m)^7.

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%I A022731 #12 Sep 08 2022 08:44:46
%S A022731 1,7,42,203,889,3535,13209,46551,156905,507787,1588594,4819003,
%T A022731 14231294,41007134,115589904,319284693,865781826,2307766118,
%U A022731 6054769679,15652436765,39909873983,100451866962
%N A022731 Expansion of Product_{m>=1} 1/(1 - m*q^m)^7.
%H A022731 G. C. Greubel, <a href="/A022731/b022731.txt">Table of n, a(n) for n = 0..1000</a>
%F A022731 G.f.: exp(7*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 07 2018
%t A022731 With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^-7, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Jul 25 2018 *)
%o A022731 (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1-n*q^n)^-7)) \\ _G. C. Greubel_, Jul 25 2018
%o A022731 (Magma) n:=50; R<x>:=PowerSeriesRing(Integers(), n); Coefficients(R!(&*[(1/(1-m*x^m))^7:m in [1..n]])); // _G. C. Greubel_, Jul 25 2018
%Y A022731 Column k=7 of A297328.
%K A022731 nonn
%O A022731 0,2
%A A022731 _N. J. A. Sloane_