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A036282 Write cosec x = 1/x + Sum e_n x^(2n-1)/(2n-1)!; sequence gives numerators of e_n. 5
1, 7, 31, 127, 511, 1414477, 8191, 118518239, 5749691557, 91546277357, 162912981133, 1982765468311237, 22076500342261, 455371239541065869, 925118910976041358111, 16555640865486520478399, 1302480594081611886641, 904185845619475242495834469891 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Contribution from Johannes W. Meijer, May 24 2009: (Start)

Absolute value of numerator of [2^(2n-1) - 1] * Bernoulli(2n)/n.

(End)

REFERENCES

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).

LINKS

Table of n, a(n) for n=1..18.

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. 75 (4.3.68).

Simon Plouffe, On the values of the functions ... [zeta and Gamma] ..., arXiv preprint arXiv:1310.7195, 2013

Duane W. DeTemple, Shun-Hwa Wang, Half-integer approximations for the partial sums of harmonic series, J. Math. Anal. Applic. 160 (1991) 149-156

Eric Weisstein's World of Mathematics, Riemann-Siegel Functions

EXAMPLE

x^(-1)+1/6*x+7/360*x^3+31/15120*x^5+...

MATHEMATICA

a[n_] := Abs[ Numerator[ (2^(2*n-1)-1) * BernoulliB[2*n]/n ] ]; Table[a[n], {n, 1, 18}] (* Jean-Fran├žois Alcover, May 31 2013, after Johannes W. Meijer *)

CROSSREFS

Cf. A036280-A036283.

Contribution from Johannes W. Meijer, May 24 2009: (Start)

Equals the absolute values of the numerators of the LS1[ -2*m,n=1] matrix coefficients of A160487 for m = 1, 2, .. ,.

(End)

Sequence in context: A002147 A169785 A083420 * A033474 A001896 A180147

Adjacent sequences:  A036279 A036280 A036281 * A036283 A036284 A036285

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Title corrected and offset changed by Johannes W. Meijer, May 21 2009

STATUS

approved

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Last modified July 29 04:40 EDT 2014. Contains 245018 sequences.