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%I #12 Oct 07 2019 11:45:16
%S 0,0,1,16,232,3328,47956,696256,10185824,150050816,2224086242,
%T 33144506016,496287233040,7462288270848,112621324354952,
%U 1705306407267200,25898042412463808,394353145059565568
%N Expansion of q^2 in powers of m/16 where q is Jacobi nome and m is the parameter.
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 591.
%H Vaclav Kotesovec, <a href="/A119463/b119463.txt">Table of n, a(n) for n = 0..600</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%F Expansion of exp(2*Pi*i*tau) in powers of lambda(tau)/16 where lambda is elliptic lambda function
%F G.f.: exp(-2*Pi*agm(1, sqrt(1-16x))/agm(1, sqrt(16x))).
%t CoefficientList[Series[EllipticNomeQ[16*x]^2, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 07 2019 *)
%o (PARI) {a(n)=if(n<2, 0, n-=2; polcoeff( serreverse(x*prod(k=1, n, (1+x^k)^(-1)^k, 1+x*O(x^n))^8)^2, n+2))}
%o (PARI) {a(n)=n-=2; if(n<=0, n==0, polcoeff( subst(serreverse(1/ellj(x+x*O(x^n))),x,(x-16*x^2)^2/(1-16*x+256*x^2)^3), n+2))}
%Y Cf. A005797.
%K nonn
%O 0,4
%A _Michael Somos_, May 20 2006
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