A186247 n-th derivative of sec(x)^x at x=0.

1, 0, 0, 3, 0, 10, 90, 112, 1680, 10008, 52920, 503096, 3750120, 32707376, 317212896, 3115701240, 33444028800, 378122087104, 4501793066688, 56612612281984, 746976298243200, 10328059310335872, 149410872069250176, 2255298661460780288, 35481940129572393600, 580614509996338380800

Offset

0,4

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 0..444

Formula

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

a(n) ~ (2*n/Pi)^(n+Pi/2)*sqrt(2*Pi/n)*exp(-n)/Gamma(Pi/2). - Vaclav Kotesovec, Sep 25 2013

a(n) = (-1)^n * A215347(n) = |A215347(n)|. - Robert Israel, Aug 28 2015

Maple

a:= n-> n! * coeff(series(cos(x)^(-x), x, n+1), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, Aug 18 2012

Mathematica

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

Crossrefs

Cf. A215347.

Sequence in context: A327881 A215514 A215347 * A215585 A215682 A215681

Adjacent sequences: A186244 A186245 A186246 * A186248 A186249 A186250

Keyword

nonn

Author

Michel Lagneau, Aug 18 2012

Status

approved