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A215347
n-th derivative of cos(x)^x at x=0.
2
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
KEYWORD
sign
AUTHOR
Michel Lagneau, Aug 14 2012
EXTENSIONS
Typo in Mathematica code fixed by Vincenzo Librandi, Oct 04 2013
STATUS
approved