A327998 a(n) = (n!/floor(n/2)!^2)^2.

1, 1, 4, 36, 36, 900, 400, 19600, 4900, 396900, 63504, 7683984, 853776, 144288144, 11778624, 2650190400, 165636900, 47869064100, 2363904400, 853369488400, 34134779536, 15053437775376, 497634306624, 263248548204096, 7312459672336, 4570287295210000, 108172480360000

Offset: 0

Author

Peter Luschny, Oct 19 2019

Keywords

• nonn

Crossrefs

Central column of A328001.

Even bisection is A002894.

Programs

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 *)

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)).