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

%I #7 Aug 15 2012 09:50:13

%S 1,0,0,-3,0,0,90,-63,0,-8880,22680,-49203,2118600,-12383280,60540480,

%T -1131841623,10857974400,-87893114400,1246674306240,-15590737021923,

%U 175749917616000,-2471071936993440,35757593223327360,-502589340005210703,7719667979121014400

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

%p f:= x-> cos(x)^sin(x):

%p b:= proc(n) b(n):= `if`(n=0, f, D(b(n-1))) end:

%p a:= n-> b(n)(0):

%p seq (a(n), n=0..20); # _Alois P. Heinz_, Aug 14 2012

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

%Y Cf. A160537.

%K sign

%O 0,4

%A _Michel Lagneau_, Aug 14 2012