A186246 - OEIS

%I #27 Sep 08 2022 08:45:55

%S -1,2,-24,720,-40320,3628800,-479001600,87178291200,-20922789888000,

%T 6402373705728000,-2432902008176640000,1124000727777607680000,

%U -620448401733239439360000,403291461126605635584000000,-304888344611713860501504000000,265252859812191058636308480000000

%N (2n+1)-th derivative of arccot(x) at x=0.

%C Also the negated (2n+1)-th derivative of arctan(x) at x=0. - _Stanislav Sykora_, Jan 06 2017

%H G. C. Greubel, <a href="/A186246/b186246.txt">Table of n, a(n) for n = 0..224</a>

%F a(n) = (-1)^(n+1)*A010050(n). - _M. F. Hasler_, Apr 22 2015

%p a:= n-> (2*n+1)! * coeftayl(arccot(x), x=0, 2*n+1):

%p seq (a(n), n=0..20);  # _Alois P. Heinz_, Aug 18 2012

%t f[x_] := ArcCot[x]; Table[Derivative[2*n+1][f][0],{n,0,17}]

%t Table[(-1)^(n + 1)*(2*n)!, {n, 0, 50}] (* _G. C. Greubel_, Aug 10 2018 *)

%o (PARI) {a(n) = if( n<0, 0, -(-1)^n * (2*n)!)}; /* _Michael Somos_, Jan 07 2017 */

%o (Magma) [(-1)^(n+1)*Factorial(2*n): n in [0..50]]; // _G. C. Greubel_, Aug 10 2018

%Y Cf. A010050.

%K sign

%O 0,2

%A _Michel Lagneau_, Aug 18 2012