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.
%I A215603 #10 May 22 2013 00:14:10
%S A215603 1,2,-2,2,10,-10,6,10,-22,58,-58,10,114,-210,270,-242,74,382,-930,
%T A215603 1474,-1542,1010,446,-2798,5682,-7718,8030,-5182,-998,11126,-23802,
%U A215603 35626,-42246,39450,-20810,-15546,69514,-133770,194918,-234106,227410,-147706,-19738,282234
%N A215603 O.g.f.: exp( Sum_{n>=1} -(sigma(2*n^2) - sigma(n^2)) * (-x)^n/n ).
%C A215603 Compare to the Jacobi theta_3 function:
%C A215603 1 + 2*Sum_{n>=1} x^(n^2) = exp( Sum_{n>=1} -(sigma(2*n) - sigma(n))*(-x)^n/n ).
%C A215603 Here sigma(n) = A000203(n) is the sum of divisors of n.
%H A215603 Paul D. Hanna, <a href="/A215603/b215603.txt">Table of n, a(n) for n = 0..1000</a>
%F A215603 O.g.f.: exp( Sum_{n>=1} -A054785(n^2)*(-x)^n/n ), where A054785(n^2) = A195585(n).
%e A215603 O.g.f.: A(x) = 1 + 2*x - 2*x^2 + 2*x^3 + 10*x^4 - 10*x^5 + 6*x^6 + 10*x^7 +...
%e A215603 where
%e A215603 log(A(x)) = 2*x - 8*x^2/2 + 26*x^3/3 - 32*x^4/4 + 62*x^5/5 - 104*x^6/6 + 114*x^7/7 - 128*x^8/8 + 242*x^9/9 - 248*x^10/10 + 266*x^11/11 - 416*x^12/12 +...+ -A054785(n^2)*(-x)^n/n +...
%o A215603 (PARI) {a(n)=polcoeff(exp(sum(m=1, n,-(sigma(2*m^2)-sigma(m^2))*(-x)^m/m)+x^2*O(x^n)),n)}
%o A215603 for(n=0,50,print1(a(n),", "))
%Y A215603 Cf. A195584, A195585, A177399, A054785, A000203; variants: A225925, A225957.
%K A215603 sign
%O A215603 0,2
%A A215603 _Paul D. Hanna_, Aug 17 2012