A372987 a(n) = (2*n)!/(n!*a(n-1)), with a(0)=1.

1, 2, 6, 20, 84, 360, 1848, 9360, 55440, 318240, 2106720, 13366080, 96909120, 668304000, 5233092480, 38761632000, 324451733760, 2558267712000, 22711621363200, 189311810688000, 1771506466329600, 15523568476416000, 152349556104345600, 1397121162877440000

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..665

Formula

a(n) = Product_{k=0..floor((n-1)/2)} 2*(2*n-4*k-1). - Andrew Howroyd, Jul 10 2024

Maple

f:= proc(n) option remember;
  (2*n)!/(n! * procname(n-1))
end proc:
f(0):= 1:
map(f, [$0..30]); # Robert Israel, Jul 09 2025

Mathematica

a[0] = 1; a[n_] := a[n] = (2n)!/(n!*a[n - 1]);
Table[a[n], {n, 0, 30}]

Prog

(PARI) a(n)=prod(k=0, (n-1)\2, 2*(2*n-4*k-1)) \\ Andrew Howroyd, Jul 10 2024

Crossrefs

Cf. A372986, A372988.

Sequence in context: A177476 A266600 A177474 * A177480 A365229 A089179

Adjacent sequences: A372984 A372985 A372986 * A372988 A372989 A372990

Keyword

nonn

Author

Clark Kimberling, Jul 09 2024

Status

approved