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A119463
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Expansion of q^2 in powers of m/16 where q is Jacobi nome and m is the parameter.
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0
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0, 0, 1, 16, 232, 3328, 47956, 696256, 10185824, 150050816, 2224086242, 33144506016, 496287233040, 7462288270848, 112621324354952, 1705306407267200, 25898042412463808, 394353145059565568
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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.
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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].
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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))).
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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))}
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CROSSREFS
| Cf. A005797.
Sequence in context: A048445 A028340 A166903 * A111096 A161591 A103975
Adjacent sequences: A119460 A119461 A119462 * A119464 A119465 A119466
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, May 20 2006
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