A356901 a(n) = (2*n)! * [x^(2*n)] arctan(x / sqrt(2))^2.

0, 1, -4, 46, -1056, 40536, -2342880, 190229040, -20655129600, 2890827273600, -506836099929600, 108811461852576000, -28078128329061888000, 8574915159297970560000, -3059025135601894018560000, 1260573112806548772591360000, -594261372327243392714342400000

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = (2*n)! * [x^(2*n)] ((log(1 + I*x/sqrt(2)) - log(1 - I*x/sqrt(2)))/2)^2.

Maple

ser := series(arctan(x / sqrt(2))^2, x, 38):
seq((2*n)! * coeff(ser, x, 2*n), n = 0..17);

Crossrefs

Sequence in context: A191870 A099023 A000657 * A001623 A188634 A331978

Adjacent sequences: A356898 A356899 A356900 * A356902 A356903 A356904

Keyword

sign

Author

Peter Luschny, Sep 03 2022

Status

approved