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.

A327747 Expansion of Product_{i>=1, j>=1} 1 / (1 + (-x)^(i*j^2)).

This page as a plain text file.
%I A327747 #5 Sep 24 2019 12:39:48
%S A327747 1,1,0,1,0,0,1,0,1,2,2,1,1,0,1,2,1,2,2,2,1,1,1,2,3,4,3,4,4,1,4,3,4,7,
%T A327747 6,7,6,4,5,5,7,9,9,9,8,7,7,7,10,14,13,12,14,10,12,16,13,20,19,20,20,
%U A327747 16,18,20,22,26,27,27,28,23,26,25,31,38,36,40
%N A327747 Expansion of Product_{i>=1, j>=1} 1 / (1 + (-x)^(i*j^2)).
%F A327747 G.f.: Product_{k>=1} 1 / (1 + (-x)^k)^A046951(k).
%t A327747 nmax = 75; CoefficientList[Series[Product[1/(1 + (-x)^k)^Length[Select[Divisors[k], IntegerQ[Sqrt[#]] &]], {k, 1, nmax}], {x, 0, nmax}], x]
%t A327747 a[n_] := a[n] = If[n == 0, 1, Sum[(-1)^k Sum[(-1)^(k/d) d Length[Select[Divisors[d], IntegerQ[Sqrt[#]] &]], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 75}]
%Y A327747 Cf. A004101, A046951, A280451.
%K A327747 nonn
%O A327747 0,10
%A A327747 _Ilya Gutkovskiy_, Sep 23 2019