A215347 - OEIS

%I #49 Aug 28 2015 02:06:07

%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

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

%H Vincenzo Librandi and Robert Israel, <a href="/A215347/b215347.txt">Table of n, a(n) for n = 0..444</a> (n = 0 .. 50 from Vincenzo Librandi)

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

%F a(n) ~ n! * (-1)^n * (2/Pi)^(n+Pi/2)*n^(Pi/2-1)/Gamma(Pi/2). - _Vaclav Kotesovec_, Oct 02 2013

%F a(n) = (-1)^n * A186247(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..20);  # _Alois P. Heinz_, Aug 14 2012

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

%Y Cf. A186247.

%K sign

%O 0,4

%A _Michel Lagneau_, Aug 14 2012

%E Typo in Mathematica code fixed by _Vincenzo Librandi_, Oct 04 2013