A201158 E.g.f. exp(x)/(cos(x) - sin(x)).

1, 2, 6, 24, 124, 792, 6056, 53984, 549904, 6301472, 80233056, 1123714944, 17169102784, 284184941952, 5065697161856, 96747688891904, 1970927736619264, 42660873261343232, 977715195437139456, 23652447354912036864, 602304626050881977344

Offset

0,2

Comments

Sum_{n>=0} a(n)x^n/n! = exp(x)/(cos(x) - sin(x)).

Links

Table of n, a(n) for n=0..20.

Formula

Sum_{n>=0} a(n)x^n/n! = exp(x)/(cos(x) - sin(x)).

exp(x)/(cos(x) - sin(x)) = 1/G(0); G(k) = 1-2*x/(4*k+1+x*(4*k+1)/(2*(2*k+1)-x-2*(x^2)*(2*k+1)/((x^2)-(2*k+2)*(4*k+3)/G(k+1)))); (continued fraction).

G.f.: 1/G(0) where G(k) = 1 - 2*x*(k+1) - 2*x^2*(k+1)^2/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Jan 12 2013

a(n) ~ n! * exp(Pi/4)*2^(2*n+3/2)/Pi^(n+1). - Vaclav Kotesovec, Jun 27 2013

G.f.: T(0)/(1-2*x), where T(k) = 1 - 2*x^2*(k+1)^2/(2*x^2*(k+1)^2 - (1 - 2*x - 2*x*k)*(1 - 4*x - 2*x*k)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 29 2013

Maple

A:=series(exp(x)/(cos(x)-sin(x)), x, 40);
G(x):=A : f[0]:=G(x): for n from 1 to 41 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..40);

Mathematica

nn = 30; Range[0, nn]! CoefficientList[Series[Exp[x]/(Cos[x] - Sin[x]), {x, 0, nn}], x] (* T. D. Noe, Dec 05 2011 *)

Crossrefs

Sequence in context: A144251 A304198 A243806 * A356634 A191343 A368761

Adjacent sequences: A201155 A201156 A201157 * A201159 A201160 A201161

Keyword

nonn

Author

Sergei N. Gladkovskii, Nov 27 2011

Status

approved