|
%I #29 Sep 08 2022 08:44:37
%S 1,1,1,3,5,25,61,427,1385,12465,50521,555731,2702765,35135945,
%T 199360981,2990414715,19391512145,329655706465,2404879675441,
%U 45692713833379,370371188237525,7777794952988025,69348874393137901,1595024111042171723,15514534163557086905
%N Expansion of (1+x)/cos(x).
%H Vincenzo Librandi, <a href="/A009002/b009002.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: (1-x^2)/U(0) where U(k)= 1 - x/(1 - x/(x + (2*k+1)*(2*k+2)/U(k+1)) ; (continued fraction, 3-step). - _Sergei N. Gladkovskii_, Oct 17 2012
%F a(n) ~ n! * 2^n * (Pi + 2 + (-1)^(n+1) * (Pi - 2)) / Pi^(n+1). - _Vaclav Kotesovec_, Jan 22 2015
%p seq(coeff(series(factorial(n)*(1+x)/cos(x), x,n+1),x,n),n=0..25); # _Muniru A Asiru_, Jul 21 2018
%t With[{nn=40}, Take[CoefficientList[Series[(1 + x)/Cos[x], {x, 0, nn}], x] Range[0, nn]!]] (* _Vincenzo Librandi_, Oct 24 2012 *)
%o (PARI) x='x+O('x^30); Vec(serlaplace((1+x)/cos(x))) \\ _G. C. Greubel_, Jul 21 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1+x)/Cos(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 21 2018
%K nonn
%O 0,4
%A _R. H. Hardin_
%E Extended and formatted by _Olivier Gérard_, Mar 15 1997
%E More terms from _Ralf Stephan_, Mar 08 2004
|
