A215347 n-th derivative of cos(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

Offset

0,4

Links

Vincenzo Librandi and Robert Israel, Table of n, a(n) for n = 0..444 (n = 0 .. 50 from Vincenzo Librandi)

Formula

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

a(n) ~ n! * (-1)^n * (2/Pi)^(n+Pi/2)*n^(Pi/2-1)/Gamma(Pi/2). - Vaclav Kotesovec, Oct 02 2013

a(n) = (-1)^n * A186247(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..20);  # Alois P. Heinz, Aug 14 2012

Mathematica

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

Crossrefs

Cf. A186247.

Sequence in context: A302693 A327881 A215514 * A186247 A215585 A215682

Adjacent sequences: A215344 A215345 A215346 * A215348 A215349 A215350

Keyword

sign

Author

Michel Lagneau, Aug 14 2012

Extensions

Typo in Mathematica code fixed by Vincenzo Librandi, Oct 04 2013

Status

approved