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A119463
Expansion of q^2 in powers of m/16 where q is Jacobi nome and m is the parameter.
1
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
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
KEYWORD
nonn
AUTHOR
Michael Somos, May 20 2006
STATUS
approved