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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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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math.Series 55, Tenth Printing, December 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, December 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, December 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.
Adjacent sequences: A005794 A005795 A005796 this_sequence A005798 A005799 A005800
Sequence in context: A143868 A130591 A048665 this_sequence A052659 A113376 A093103
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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