A329964 a(n) = (n!/floor(1+n/2)!)^2.

1, 1, 1, 9, 16, 400, 900, 44100, 112896, 9144576, 25401600, 3073593600, 9032601600, 1526509670400, 4674935865600, 1051860569760000, 3324398837760000, 960751264112640000, 3112834095724953600, 1123733108556708249600, 3714820193575895040000

Offset: 0

Author

Peter Luschny, Dec 04 2019

Keywords

• nonn

Crossrefs

Cf. A262033.

Programs

Maple

A329964 := n -> (n!/floor(1+n/2)!)^2:
seq(A329964(n), n=0..20);

Mathematica

a[n_] := (n!/Floor[1 + n/2]!)^2; Array[a, 20, 0] (* Amiram Eldar, Dec 04 2022 *)

Formula

a(n) = A262033(n)^2.

Sum_{n>=0} 1/a(n) = 29/16 + (3/16)*Pi*StruveL(-1, 1/2) + (57/64)*Pi*StruveL(0, 1/2) + (1/4)*Pi*StruveL(1, 1/2), where StruveL is the modified Struve function. - Amiram Eldar, Dec 04 2022