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%I #20 Feb 01 2022 21:52:58
%S 1,1,1,13,17,97,1247,4937,6673,1058467,1380290071,3216636877,
%T 536799743,8113510922983,448402165451,39917099698166381,
%U 841245146920202183,1449011221261558349,5272145758556532286373,59293985401199969565319,11617394997961948860617
%N Numerators of coefficients of expansion of sinh(x)/sin(x) (even powers only).
%H G. C. Greubel, <a href="/A069853/b069853.txt">Table of n, a(n) for n = 0..290</a>
%H Alan Richard Baker, <a href="https://doi.org/10.1093/acprof:oso/9780198778592.003.0012">Non-Optional Projects: Mathematical and Ethical</a>, Explanation In Ethics And Mathematics: Debunking And Dispensability (2016), 220-235.
%e G.f. = 1 + (1/3)*x^2 + (1/18)*x^4 + (13/1890)*x^6 + (17/22680)*x^8 + (97/1247400)*x^10 + ...
%p a:= n-> numer(coeff(series(sinh(x)/sin(x), x, 2*n+2), x, 2*n)):
%p seq(a(n), n=0..24); # _Alois P. Heinz_, Feb 01 2022
%t With[{m=60}, CoefficientList[Series[Sinh[x]/Sin[x], {x,0,m}], x]][[1 ;; ;; 2]]//Numerator (* _G. C. Greubel_, Jan 31 2022 *)
%o (Magma)
%o m:=60; R<x>:=PowerSeriesRing(Rationals(), m);
%o b:= Coefficients(R!( Sinh(x)/Sin(x) ));
%o [Numerator( b[2*n-1] ): n in [1..Floor((m-2)/2)]]; // _G. C. Greubel_, Jan 31 2022
%o (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
%Y Cf. A069854.
%Y Bisection of A007418.
%K easy,frac,nonn
%O 0,4
%A _Benoit Cloitre_, May 03 2002
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