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%I #11 Jul 29 2018 20:46:43
%S 0,1,-3,5,-8,9,-11,16,-15,18,-24,21,-23,32,-30,29,-41,33,-35,53,-39,
%T 41,-56,48,-54,65,-51,53,-72,66,-64,80,-63,65,-102,69,-72,103,-75,90,
%U -104,81,-83,117,-111,89,-120,96,-95,146,-99,112,-143,105,-126,144
%N Expansion of x^1 * (1-x^1) / (1+x^1)^2 - x^4 * (1-x^3) * (1+x^3)^2 + x^9 * (1-x^5) / (1+x^5)^2 - ... in powers of x.
%C In [Andrews and Berndt (2005)] take the derivative of equation (12.4.23) with respect to a, set a=-1, and multiply by q.
%D G. E. Andrews, B. C. Berndt, Ramanujan's lost notebook, Part I, Springer, New York, 2005, MR2135178 (2005m:11001) See p. 278, Equ. (12.4.23).
%H G. C. Greubel, <a href="/A292526/b292526.txt">Table of n, a(n) for n = 0..2500</a>
%F G.f.: Sum_{k>0} -(-1)^k * x^(k^2) * (1 - x^(2*k-1)) / (1 + x^(2*k-1))^2.
%F G.f. of A292511 is the product of the g.f. of A015128 and this g.f. divided by x.
%e G.f. = x - 3*x^2 + 5*x^3 - 8*x^4 + 9*x^5 - 11*x^6 + 16*x^7 - 15*x^8 + 18*x^9 + ...
%p seq(coeff(series(add(-(-1)^k*x^(k^2)*(1-x^(2*k-1))/(1+x^(2*k-1))^2,k=1..n), x,n+1),x,n),n=0..60); # _Muniru A Asiru_, Jul 29 2018
%t a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Sum[ -(-1)^k x^k^2 (1 - x^(2 k - 1)) / (1 + x^(2 k - 1))^2, {k, Sqrt@n}], {x, 0, n}]];
%o (PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=1, sqrtint(n), -(-1)^k * x^(k^2) * (1 - x^(2*k-1) + x * O(x^(n-k^2))) / (1 + x^(2*k-1))^2), n))};
%Y Cf. A015128, A292511.
%K sign
%O 0,3
%A _Michael Somos_, Sep 18 2017
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