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

Author

Benoit Cloitre, May 03 2002

Keywords

• easy
• frac
• nonn

Examples

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

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.

Crossrefs

Cf. A069854.

Bisection of A007418.

Programs

Magma

m:=60; R:=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

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 *)

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