A367963 a(n) = Sum_{j=0..n} (2*n)! / (n!*(n - j)!).

1, 4, 30, 320, 4550, 82152, 1808268, 47018400, 1410564870, 47959254200, 1822451844356, 76542978168384, 3520976998449820, 176048849932891600, 9506637896416263000, 551384997992298371520, 34185869875523100114630, 2256267411784526941171800, 157938718824916894957161300

Offset: 0

Author

Peter Luschny, Dec 06 2023

Keywords

• nonn

Crossrefs

Cf. A367962.

Programs

Maple

a := n -> add((2*n)!/(n!*(n-j)!), j = 0..n):
seq(a(n), n = 0..18);

Mathematica

Table[Sum[(2n)!/(n!(n-j)!),{j,0,n}],{n,0,20}] (* Harvey P. Dale, Feb 10 2024 *)

Formula

a(n) = (exp(1) * Gamma(n + 1, 1) * Gamma(2*n + 1)) / Gamma(n + 1)^2.

a(n) * n! = A367962(2*n, n).