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

0,2

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

Formula

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

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 *)

Prog

(PARI) {a(n) = if( n<0, 0, -(-1)^n * (2*n)!)}; /* Michael Somos, Jan 07 2017 */
(Magma) [(-1)^(n+1)*Factorial(2*n): n in [0..50]]; // G. C. Greubel, Aug 10 2018

Crossrefs

Cf. A010050.

Sequence in context: A279236 A279309 A010050 * A012161 A009724 A177771

Adjacent sequences: A186243 A186244 A186245 * A186247 A186248 A186249

Keyword

sign

Author

Michel Lagneau, Aug 18 2012

Status

approved