A119463 Expansion of q^2 in powers of m/16 where q is Jacobi nome and m is the parameter.

0, 0, 1, 16, 232, 3328, 47956, 696256, 10185824, 150050816, 2224086242, 33144506016, 496287233040, 7462288270848, 112621324354952, 1705306407267200, 25898042412463808, 394353145059565568

Offset: 0

Author

Michael Somos, May 20 2006

Keywords

• nonn

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 591.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..600
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A005797.

Programs

Mathematica

CoefficientList[Series[EllipticNomeQ[16*x]^2, {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 07 2019 *)

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))}

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))}

Formula

Expansion of exp(2*Pi*i*tau) in powers of lambda(tau)/16 where lambda is elliptic lambda function

G.f.: exp(-2*Pi*agm(1, sqrt(1-16x))/agm(1, sqrt(16x))).