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

0,3

Links

Table of n, a(n) for n=0..26.

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

Central column of A328001.

Even bisection is A002894.

Sequence in context: A027644 A174426 A198642 * A274891 A062182 A308531

Adjacent sequences: A327995 A327996 A327997 * A327999 A328000 A328001

Keyword

nonn

Author

Peter Luschny, Oct 19 2019

Status

approved