A186246 (2n+1)-th derivative of arccot(x) at x=0.

-1, 2, -24, 720, -40320, 3628800, -479001600, 87178291200, -20922789888000, 6402373705728000, -2432902008176640000, 1124000727777607680000, -620448401733239439360000, 403291461126605635584000000, -304888344611713860501504000000, 265252859812191058636308480000000

Offset: 0

Author

Michel Lagneau, Aug 18 2012

Keywords

• sign

Comments

Also the negated (2n+1)-th derivative of arctan(x) at x=0. - Stanislav Sykora, Jan 06 2017

Links

• G. C. Greubel, Table of n, a(n) for n = 0..224

Crossrefs

Cf. A010050.

Programs

Magma

[(-1)^(n+1)*Factorial(2*n): n in [0..50]]; // G. C. Greubel, Aug 10 2018

Maple

a:= n-> (2*n+1)! * coeftayl(arccot(x), x=0, 2*n+1):
seq (a(n), n=0..20);  # Alois P. Heinz, Aug 18 2012

Mathematica

f[x_] := ArcCot[x]; Table[Derivative[2*n+1][f][0],{n,0,17}]
Table[(-1)^(n + 1)*(2*n)!, {n, 0, 50}] (* G. C. Greubel, Aug 10 2018 *)

PARI

{a(n) = if( n<0, 0, -(-1)^n * (2*n)!)}; /* Michael Somos, Jan 07 2017 */

Formula

a(n) = (-1)^(n+1)*A010050(n). - M. F. Hasler, Apr 22 2015