This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A190195 #21 Sep 19 2023 20:16:04
%S A190195 1,-1,7,-139,5473,-51103,34988647,-4784061619,17782347217,
%T A190195 -203906055033841,4586025046220899,-234038275571853889,
%U A190195 9127322584507530151393,-4621897483978366951337161,390009953658229908025520161,-1860452328661957054823447670979,111446346975327291562408943638981,-14050053632877769956552601074149491,1269258883676324618437848731917951368967,-1408182090109327874242950762763137949746859
%N A190195 Numerators of a Taylor series expansion of 1/sqrt(cosh(x)) (even powers only).
%H A190195 Philippe Flajolet, Xavier Gourdon, and Philippe Dumas, <a href="https://doi.org/10.1016/0304-3975(95)00002-E">Mellin transforms and asymptotics: harmonic sums</a>, Special volume on mathematical analysis of algorithms. Theoret. Comput. Sci. 144 (1995), no. 1-2, 3-58.
%F A190195 a(n) = numerator(b(n)), where b(n) = Sum_{k=1..n} b(n-k)*(k/(2*n)-1)/(2*k)!, with b(0)=1. - _Tani Akinari_, Sep 17 2023
%F A190195 a(n) = numerator((-1)^n*A186491(n)/(4^n*(2*n)!)). - _Andrew Howroyd_, Sep 19 2023
%e A190195 1/sqrt(cosh(x)) = 1 - (1/4)*x^2 + (7/96)*x^4 - (139/5760)*x^6 + (5473/645120)*x^8 - (51103/16588800)*x^10 + ...
%p A190195 a:= n-> numer(coeff(series(1/sqrt(cosh(x)),x,2*n+1),x,2*n)):
%p A190195 seq(a(n), n=0..19); # _Alois P. Heinz_, Sep 19 2023
%o A190195 (Maxima) b[n]:=if n=0 then 1 else sum(b[n-k]*(k/n/2-1)/(2*k)!,k,1,n)$ a[n]:=num(b[n])$
%o A190195 makelist(a[n],n,0,20); /* _Tani Akinari_, Sep 17 2023 */
%Y A190195 Cf. A190196 (denominators), A186491.
%K A190195 sign,frac
%O A190195 0,3
%A A190195 _N. J. A. Sloane_, May 05 2011