A009002 Expansion of (1+x)/cos(x).

1, 1, 1, 3, 5, 25, 61, 427, 1385, 12465, 50521, 555731, 2702765, 35135945, 199360981, 2990414715, 19391512145, 329655706465, 2404879675441, 45692713833379, 370371188237525, 7777794952988025, 69348874393137901, 1595024111042171723, 15514534163557086905

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

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

a(n) ~ n! * 2^n * (Pi + 2 + (-1)^(n+1) * (Pi - 2)) / Pi^(n+1). - Vaclav Kotesovec, Jan 22 2015

Maple

seq(coeff(series(factorial(n)*(1+x)/cos(x), x, n+1), x, n), n=0..25); # Muniru A Asiru, Jul 21 2018

Mathematica

With[{nn=40}, Take[CoefficientList[Series[(1 + x)/Cos[x], {x, 0, nn}], x] Range[0, nn]!]] (* Vincenzo Librandi, Oct 24 2012 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace((1+x)/cos(x))) \\ G. C. Greubel, Jul 21 2018
(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

Crossrefs

Sequence in context: A356274 A249935 A364961 * A119882 A276968 A074701

Adjacent sequences: A008999 A009000 A009001 * A009003 A009004 A009005

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and formatted by Olivier Gérard, Mar 15 1997

More terms from Ralf Stephan, Mar 08 2004

Status

approved