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.

A022637 Expansion of Product_{m>=1} (1 + m*q^m)^9.

This page as a plain text file.
%I A022637 #12 Sep 08 2022 08:44:46
%S A022637 1,9,54,273,1197,4761,17577,60957,200799,633007,1920510,5633667,
%T A022637 16037700,44439840,120165858,317762553,823240341,2092864401,
%U A022637 5228118701,12848849154,31100190048,74208885351,174708121455,406132690635,932871440739,2118595079790,4759875472491
%N A022637 Expansion of Product_{m>=1} (1 + m*q^m)^9.
%H A022637 G. C. Greubel, <a href="/A022637/b022637.txt">Table of n, a(n) for n = 0..1000</a>
%F A022637 G.f.: exp(9*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - _Ilya Gutkovskiy_, Feb 08 2018
%t A022637 With[{nmax = 50}, CoefficientList[Series[Product[(1 + k*q^k)^9, {k, 1, nmax}], {q, 0, nmax}], q]] (* _G. C. Greubel_, Feb 17 2018 *)
%o A022637 (PARI) m=50; q='q+O('q^m); Vec(prod(n=1,m,(1+n*q^n)^9)) \\ _G. C. Greubel_, Feb 17 2018
%o A022637 (Magma) Coefficients(&*[(1+m*x^m)^9:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // _G. C. Greubel_, Feb 17 2018
%Y A022637 Column k=9 of A297321.
%K A022637 nonn
%O A022637 0,2
%A A022637 _N. J. A. Sloane_