A374437 a(n) = [1 - (n + s)/2]_n * [1 - (n - s)/2]_n, where s = sqrt(-n*(2 + n)) and [x]_n is the Pochhammer function.

1, 1, 6, 96, 2940, 147015, 10902528, 1124057088, 153811768320, 26974095778125, 5899429878170400, 1574248324943314944, 503433848781210320064, 190069012187712441058275, 83650190971694738227200000, 42450063041684340146700288000, 24606022217067172854917986516992

Offset: 0

Author

Peter Luschny, Aug 02 2024

Keywords

• nonn

Crossrefs

Cf. A375050, A000217.

Programs

Mathematica

a[n_] := With[{s = Sqrt[-n*(2 + n)]}, Pochhammer[1 - (n + s)/2, n] * Pochhammer[1 - (n - s)/2, n]]; Table[Simplify[a[n]], {n, 0, 16}]

Formula

a(n) = A375050(n) / A000217(n) for n > 0.

Extensions

a(16) corrected by Georg Fischer, Feb 03 2025