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Search: id:A005797
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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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+0
5
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| 0, 1, 8, 84, 992, 12514, 164688, 2232200, 30920128, 435506703, 6215660600, 89668182220, 1305109502496, 19138260194422, 282441672732656, 4191287776164504, 62496081197436736, 935823746406530603
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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LINKS
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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
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G.f.: q=q(m)=Sum_{n=1..oo} a(n)(m/16)^n.
G.f.: exp(-pi*agm(1, sqrt(1-16x)/agm(1, sqrt(16x)))).
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PROGRAM
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(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))
(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=A/(1+4*A)^2); polcoeff(serreverse(A), n))
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CROSSREFS
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Reversion of A005798. Cf. A002639.
Sequence in context: A143868 A130591 A048665 this_sequence A052659 A113376 A093103
Adjacent sequences: A005794 A005795 A005796 this_sequence A005798 A005799 A005800
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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