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A036282 Write cosec x = 1/x + Sum e_n x^(2n-1)/(2n-1)!; sequence gives numerators of e_n. 6
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

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

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)

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:1310.7195 [math.NT], 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 *)

PROG

(PARI) a(n) = abs(numerator(-2*(2^(2*n-1)-1)*bernfrac(2*n)/n)); \\ Michel Marcus, Mar 01 2015

CROSSREFS

Cf. A036280, A036282, A036283.

Cf. A160487

Sequence in context: A169785 A255282 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 March 28 13:42 EDT 2015. Contains 255986 sequences.