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A036282
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Write cosec x = 1/x + Sum_{n>=1} e_n * x^(2n-1)/(2n-1)!; sequence gives numerators of e_n.
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7
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1, 7, 31, 127, 511, 1414477, 8191, 118518239, 5749691557, 91546277357, 162912981133, 1982765468311237, 22076500342261, 455371239541065869, 925118910976041358111, 16555640865486520478399, 1302480594081611886641, 904185845619475242495834469891
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OFFSET
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1,2
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COMMENTS
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Absolute value of numerator of [2^(2n-1) - 1] * Bernoulli(2n)/n.
Equals the absolute values of the numerators of the LS1[ -2*m,n=1] matrix coefficients of A160487 for m = 1, 2, .. ,.
(End)
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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, 1972, p. 75 (4.3.68).
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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].
Eric Weisstein's World of Mathematics, Cosecant
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EXAMPLE
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cosec x
= x^(-1) + 1/6*x + 7/360*x^3 + 31/15120*x^5 + ...
= x^(-1) + 1/6 * x/1! + 7/60 * x^3/3! + 31/126 * x^5/5! + ...
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MAPLE
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a:= n-> (m-> numer(coeff(series(csc(x), x, m+1), x, m)*m!))(2*n-1):
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MATHEMATICA
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PROG
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(PARI) a(n) = abs(numerator((2^(2*n-1)-1)*bernfrac(2*n)/n)); \\ Michel Marcus, Mar 01 2015
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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