OFFSET
1,3
FORMULA
E.g.f.: sec(x)/(1-x) = 1/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
E.g.f.: (1-1/Q(0))/(1-x), where Q(k)= 1 - (2*k+1)*(2*k+2)/x^2 + 1/x^2*(2*k+1)*(2*k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, May 01 2013
a(n) ~ n!/cos(1). - Vaclav Kotesovec, Jun 27 2013
MAPLE
G(x):=sec(x)/(1-x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..21); #
MATHEMATICA
CoefficientList[Series[1/(Cos[x]*(1-x)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)
PROG
(PARI) x='x+O('x^66); Vec(serlaplace(1/(cos(x)*(1-x)))) \\ Joerg Arndt, May 01 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Zerinvary Lajos, Apr 03 2009
STATUS
approved