A069853 Numerators of coefficients of expansion of sinh(x)/sin(x) (even powers only).

1, 1, 1, 13, 17, 97, 1247, 4937, 6673, 1058467, 1380290071, 3216636877, 536799743, 8113510922983, 448402165451, 39917099698166381, 841245146920202183, 1449011221261558349, 5272145758556532286373, 59293985401199969565319, 11617394997961948860617

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..290

Alan Richard Baker, Non-Optional Projects: Mathematical and Ethical, Explanation In Ethics And Mathematics: Debunking And Dispensability (2016), 220-235.

Example

G.f. = 1 + (1/3)*x^2 + (1/18)*x^4 + (13/1890)*x^6 + (17/22680)*x^8 + (97/1247400)*x^10 + ...

Maple

a:= n-> numer(coeff(series(sinh(x)/sin(x), x, 2*n+2), x, 2*n)):
seq(a(n), n=0..24);  # Alois P. Heinz, Feb 01 2022

Mathematica

With[{m=60}, CoefficientList[Series[Sinh[x]/Sin[x], {x, 0, m}], x]][[1 ;; ;; 2]]//Numerator (* G. C. Greubel, Jan 31 2022 *)

Prog

(Magma)
m:=60; R<x>:=PowerSeriesRing(Rationals(), m);
b:= Coefficients(R!( Sinh(x)/Sin(x) ));
[Numerator( b[2*n-1] ): n in [1..Floor((m-2)/2)]]; // G. C. Greubel, Jan 31 2022
(Sage) [numerator( ( sinh(x)/sin(x) ).series(x, 2*n+3).list()[2*n] ) for n in (0..60)] # G. C. Greubel, Jan 31 2022

Crossrefs

Cf. A069854.

Bisection of A007418.

Sequence in context: A214393 A060569 A108265 * A175791 A356791 A289866

Adjacent sequences: A069850 A069851 A069852 * A069854 A069855 A069856

Keyword

easy,frac,nonn

Author

Benoit Cloitre, May 03 2002

Status

approved