A186247 - OEIS

%I #19 Aug 28 2015 02:05:56

%S 1,0,0,3,0,10,90,112,1680,10008,52920,503096,3750120,32707376,

%T 317212896,3115701240,33444028800,378122087104,4501793066688,

%U 56612612281984,746976298243200,10328059310335872,149410872069250176,2255298661460780288,35481940129572393600,580614509996338380800

%N n-th derivative of sec(x)^x at x=0.

%C sec(x) = 1/cos(x).

%H Robert Israel, <a href="/A186247/b186247.txt">Table of n, a(n) for n = 0..444</a>

%F E.g.f.: cos(x)^(-x).

%F a(n) ~ (2*n/Pi)^(n+Pi/2)*sqrt(2*Pi/n)*exp(-n)/Gamma(Pi/2). - _Vaclav Kotesovec_, Sep 25 2013

%F a(n) = (-1)^n * A215347(n) = |A215347(n)|. - _Robert Israel_, Aug 28 2015

%p a:= n-> n! * coeff(series(cos(x)^(-x), x, n+1), x, n):

%p seq(a(n), n=0..30);  # _Alois P. Heinz_, Aug 18 2012

%t f[x_] := Sec[x]^x; Table[Derivative[n] [f][0],{n,0,25}]

%Y Cf. A215347.

%K nonn

%O 0,4

%A _Michel Lagneau_, Aug 18 2012