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A005797
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Expansion of Jacobi nome q in terms of parameter m/16.
(Formerly M4561)
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4
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0, 1, 8, 84, 992, 12514, 164688, 2232200, 30920128, 435506703, 6215660600, 89668182220, 1305109502496, 19138260194422, 282441672732656, 4191287776164504, 62496081197436736, 935823746406530603
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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.
B. C. Berndt, Ramanujan's theory of theta-functions, Theta functions: from the classical to the modern, Amer. Math. Soc., Providence, RI, 1993, pp. 1-63. MR 94m:11054.
C. L. Mallows (colinm(AT)research.avayalabs.com), personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, 1972, p. 591.
Index entries for reversions of series
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FORMULA
| G.f.: q = q(m) = Sum_{n=0..oo} a(n) * (m/16)^n.
G.f.: exp( -pi * agm(1, sqrt(1 - 16 * x) / agm(1, sqrt( 16*x )))).
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EXAMPLE
| x + 8*x^2 + 84*x^3 + 992*x^4 + 12514*x^5 + 164688*x^6 + 2232200*x^7 + ...
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MATHEMATICA
| a[ n_] := SeriesCoefficient[ EllipticNomeQ[ 16 x], {x, 0 , n}] (* Michael Somos, Jul 11 2011 *)
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PROG
| (PARI) {a(n) = if( n<1, 0, polcoeff( serreverse( x * prod(k=1, n-1, (1 + x^k)^(-1)^k, 1 + x * O(x^n))^8), n))} /* Michael Somos, Jul 19 2002 */
(PARI) {a(n) = local(A, m); if( n<1, 0, m=1; A = x + O(x^2); while( m<n, m*=2; A = sqrt( subst(A, x, x^2)); A /= (1 + 4*A)^2); polcoeff( serreverse(A), n))} /* Michael Somos, Mar 18 2003 */
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CROSSREFS
| Reversion of A005798. Cf. A002639.
Sequence in context: A143868 A130591 A048665 * A052659 A113376 A205311
Adjacent sequences: A005794 A005795 A005796 * A005798 A005799 A005800
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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