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

0,4

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].

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))).

Mathematica

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

Prog

(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))}

Crossrefs

Cf. A005797.

Sequence in context: A166903 A230234 A274467 * A292341 A222389 A222938

Adjacent sequences: A119460 A119461 A119462 * A119464 A119465 A119466

Keyword

nonn

Author

Michael Somos, May 20 2006

Status

approved