This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A036282 Write cosec x = 1/x + Sum_{n>=1} e_n * x^(2n-1)/(2n-1)!; sequence gives numerators of e_n. 7
 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 Seiichi Manyama, Table of n, a(n) for n = 1..275 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). R. P. Brent, Asymptotic approximation of central binomial coefficients with rigorous error bounds, arXiv:1608.04834 [math.NA], 2016. Duane W. DeTemple, Shun-Hwa Wang, Half-integer approximations for the partial sums of harmonic series, J. Math. Anal. Applic. 160 (1991) 149-156 Simon Plouffe, On the values of the functions zeta and gamma, arXiv:1310.7195 [math.NT], 2013. Eric Weisstein's World of Mathematics, Cosecant Eric Weisstein's World of Mathematics, Riemann-Siegel Function Wikipedia, Trigonometric functions EXAMPLE 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! + ... MAPLE a:= n-> (m-> numer(coeff(series(csc(x), x, m+1), x, m)*m!))(2*n-1): seq(a(n), n=1..20);  # Alois P. Heinz, Jun 21 2018 MATHEMATICA a[n_] := Abs[ Numerator[ (2^(2*n-1)-1) * BernoulliB[2*n]/n ] ]; Table[a[n], {n, 1, 18}] (* Jean-François Alcover, May 31 2013, after Johannes W. Meijer *) PROG (PARI) a(n) = abs(numerator((2^(2*n-1)-1)*bernfrac(2*n)/n)); \\ Michel Marcus, Mar 01 2015 CROSSREFS Cf. A036280, A036281, A036283. Cf. A160487. Differs from A282898. Sequence in context: A083420 A277002 A282898 * A033474 A001896 A262630 Adjacent sequences:  A036279 A036280 A036281 * A036283 A036284 A036285 KEYWORD nonn,frac,easy AUTHOR EXTENSIONS Title corrected and offset changed by Johannes W. Meijer, May 21 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 18 13:31 EDT 2019. Contains 328161 sequences. (Running on oeis4.)