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A274656
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Denominators of coefficients of z^n for the expansion of Fricke's hypergeometric function F_1(1/2,1/2;z).
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2
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1, 2, 64, 768, 98304, 655360, 10485760, 293601280, 30064771072, 1082331758592, 86586540687360, 60473139527680, 34832528367943680, 362258295026614272, 644014746713980928, 2576058986855923712, 5275768805080931762176, 32613843522318487257088
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OFFSET
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0,2
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COMMENTS
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For the denominators of the coefficients of z^n/n! for the expansion of F_1(1/2,1/2;z) see A274654.
See the main entry A274653 (with A274654) for the definition of Fricke's hypergeometric function F_1(a,b;z) with the recurrence and details on F_1(1/2,1/2;z).
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REFERENCES
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LINKS
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FORMULA
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a(n) = denominator(R(n)), where the rationals (in lowest terms) are R(n) = [z^n]F_1(1/2,1/2;z), and the recurrence for R(n) = r(n)/n! is obtained from the one given for r(n) in A274653.
R(n) = ((2*n-1)/(2*n))^2*R(n-1) + 2*C(n)/(n*(2*n-1)), n >= 1, R(0) = 0, with C(n) = ((2*n)!)^2 / (n!^4*2^(4*n)).
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EXAMPLE
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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STATUS
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approved
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