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
KEYWORD
nonn
AUTHOR
Michael Somos, May 20 2006
STATUS
approved