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A159039 E.g.f. sec(x)/(1-x) = 1/( cos(x) * (1-x) ). 0
1, 1, 3, 9, 41, 205, 1291, 9037, 73681, 663129, 6681811, 73499921, 884701817, 11501123621, 161215091675, 2418226375125, 38711013514145, 658087229740465, 11847975015003811, 225111525285072409, 4502600876889685705, 94554618414683399805, 2080270953997427933611 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..23.

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

Sequence in context: A274739 A012246 A012099 * A074502 A109743 A139150

Adjacent sequences:  A159036 A159037 A159038 * A159040 A159041 A159042

KEYWORD

nonn

AUTHOR

Zerinvary Lajos, Apr 03 2009

STATUS

approved

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Last modified April 5 13:26 EDT 2020. Contains 333241 sequences. (Running on oeis4.)