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A356901
a(n) = (2*n)! * [x^(2*n)] arctan(x / sqrt(2))^2.
0
0, 1, -4, 46, -1056, 40536, -2342880, 190229040, -20655129600, 2890827273600, -506836099929600, 108811461852576000, -28078128329061888000, 8574915159297970560000, -3059025135601894018560000, 1260573112806548772591360000, -594261372327243392714342400000
OFFSET
0,3
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
KEYWORD
sign
AUTHOR
Peter Luschny, Sep 03 2022
STATUS
approved