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%I #16 Feb 01 2022 21:53:04
%S 1,3,18,1890,22680,1247400,157172400,6129723600,81729648000,
%T 127932046704000,1646485441080480000,37869165144851040000,
%U 62372742591519360000,9304453876089900528000000,5075156659685400288000000,4459030689216262044805920000000
%N Denominators of coefficients of expansion of sinh(x)/sin(x) (even powers only).
%H G. C. Greubel, <a href="/A069854/b069854.txt">Table of n, a(n) for n = 0..230</a>
%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-> denom(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]]//Denominator (* _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 [Denominator( b[2*n-1] ): n in [1..Floor((m-2)/2)]]; // _G. C. Greubel_, Jan 31 2022
%o (Sage) [denominator( ( 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. A069853.
%K easy,frac,nonn
%O 0,2
%A _Benoit Cloitre_, May 03 2002
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