OFFSET
0,3
FORMULA
a(n) = [x^n] (2/(Pi*(1 - 16*x^2)^2))*(2*x*EllipticE(4*x) + (16*x^2 - 1)*(16*x^2 - 1 + x)*EllipticK(4*x)).
MAPLE
seq((n!/iquo(n, 2)!^2)^2, n = 0..26); # Or:
gf := (2/(Pi*(1 - 16*x^2)^2))*(2*x*EllipticE(4*x) + (16*x^2 - 1)*(16*x^2 - 1 + x)* EllipticK(4*x)): ser := series(gf, x, 30): seq(coeff(ser, x, n), n = 0..26);
MATHEMATICA
Table[(n!/(Floor[n/2]!)^2)^2, {n, 0, 30}] (* Harvey P. Dale, May 11 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Oct 19 2019
STATUS
approved