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 A193538 #9 Mar 30 2012 18:37:28
%S A193538 1,2,6,20,46,116,284,632,1414,3102,6536,13636,28020,56300,111888,
%T A193538 219608,424694,813104,1540818,2888060,5366072,9884616,18050428,
%U A193538 32713048,58851972,105113942,186505864,328821408,576153008,1003687444,1738735728,2995837872
%N A193538 O.g.f.: exp( Sum_{n>=1} (sigma(2*n)-sigma(n))^2/2 * x^n/n ).
%C A193538 Here sigma(n) = A000203(n) is the sum of divisors of n. Compare g.f. to the formula for Jacobi theta_4(x) given by
%C A193538 theta_4(x) = exp( Sum_{n>=1} (sigma(n)-sigma(2*n))*x^n/n )
%C A193538 where theta_4(x) = 1 + Sum_{n>=1} 2*(-x)^(n^2).
%F A193538 Self-convolution yields A177398.
%e A193538 G.f.: A(x) = 1 + 2*x + 6*x^2 + 20*x^3 + 46*x^4 + 116*x^5 + 284*x^6 +...
%e A193538 log(A(x)) = 2^2*x/2 + 4^2*x^2/4 + 8^2*x^3/6 + 8^2*x^4/8 + 12^2*x^5/10 + 16^2*x^6/12 + 16^2*x^7/14 + 16^2*x^8/16 + 26^2*x^9/18 +...+ A054785(n)^2/2*x^n/n +...
%o A193538 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, (sigma(2*m)-sigma(m))^2/2*x^m/m)+x*O(x^n)), n)}
%Y A193538 Cf. A177398, A054785, A186690.
%K A193538 nonn
%O A193538 0,2
%A A193538 _Paul D. Hanna_, Jul 29 2011