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.

A022695 Expansion of Product_{m>=1} (1 + m*q^m)^-3.

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%I A022695 #30 Sep 08 2022 08:44:46
%S A022695 1,-3,0,-1,18,-12,11,-54,84,-218,243,-270,1046,-1524,1692,-3547,7722,
%T A022695 -11868,15364,-29130,52416,-83467,125514,-190716,380406,-628290,
%U A022695 808218,-1394734,2585895,-3784566,5678826,-9514614,15635424,-25331990,37563810,-57387042,100038145,-156346224
%N A022695 Expansion of Product_{m>=1} (1 + m*q^m)^-3.
%C A022695 This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = 3, g(n) = -n. - _Seiichi Manyama_, Dec 30 2017
%H A022695 Seiichi Manyama, <a href="/A022695/b022695.txt">Table of n, a(n) for n = 0..1000</a>
%F A022695 G.f.: exp(-3*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 08 2018
%t A022695 With[{nmax=50}, CoefficientList[Series[Product[1/(1+k*q^k)^3, {k,1,nmax}], {q, 0, nmax}],q]] (* _G. C. Greubel_, Feb 25 2018 *)
%o A022695 (PARI) first(n) = Vec(prod(m=1, n, (1+m*x^m)^(-3)) + O(x^n)) \\ _Iain Fox_, Dec 30 2017
%o A022695 (Magma) Coefficients(&*[1/(1+m*x^m)^3:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 25 2018
%Y A022695 Column k=3 of A297325.
%K A022695 sign
%O A022695 0,2
%A A022695 _N. J. A. Sloane_