%I #2 Apr 30 2014 01:35:19
%S 1,-3,0,8,-9,3,8,-27,24,19,-48,24,17,-54,57,46,-147,51,145,-222,123,
%T 160,-459,315,306,-678,360,326,-870,633,612,-1581,723,1286,-2301,1242,
%U 1522,-3864,2451,2455,-5478,2934,2924,-7044,4599,4622,-11271,5514,8133,-15591,8508
%N Expansion of ((eta(q)eta(q^15))/(eta(q^3)eta(q^5)))^3 in powers of q.
%C G.f. A(x) satisfies 0=f(A(x),A(x^2)) where f(u,v)=u^3+v^3+uv(-1+6(u+v)-uv).
%C Euler transform of period 15 sequence [ -3,-3,0,-3,0,0,-3,-3,0,0,-3,0,-3,-3,0,...].
%D B. C. Berndt, H. H. Chan, S.-S. Huang, Incomplete Elliptic Integrals in Ramanujan's Lost Notebook, in q-series from a Contemporary Perspective, M. E. H. Ismail and D. Stanton, eds., Amer. Math. Soc., 2000, pp. 79-126.
%H B. C. Berndt, H. H. Chan, S.-S. Huang, <a href="http://www.math.uiuc.edu/~berndt/articles/ellipticintegral.pdf">Incomplete Elliptic Integrals in Ramanujan's Lost Notebook</a>.
%F G.f. x(Prod_{k>0} ((1-x^k)(1-x^(15k)))/(1-x^(3k))(1-x^(5k)))^3.
%o (PARI) a(n)=local(A); if(n<1,0,n--; A=x*O(x^n); polcoeff((eta(x+A)*eta(x^15+A)/eta(x^3+A)/eta(x^5+A))^3,n))
%K sign
%O 1,2
%A _Michael Somos_, May 28 2004
|