A361877 a(n) = binomial(2*n, n) * binomial(2*n - 1, n).

1, 2, 18, 200, 2450, 31752, 426888, 5889312, 82818450, 1181952200, 17067389768, 248817153312, 3656229836168, 54086240180000, 804670797780000, 12030722505475200, 180648817621276050, 2722858995011344200, 41179040356653045000, 624643836545795220000, 9500832753861545296200

Offset: 0

Author

Peter Luschny, Mar 27 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 0..829

Crossrefs

Cf. A002894, A000984, A001700.

Programs

Maple

A361877 := n -> binomial(2*n, n) * binomial(2*n - 1, n):
seq(A361877(n), n = 0..20);
# Alternative:
a := proc(n) option remember; ifelse(n < 2, n + 1, (4 - 2 / n)^2 * a(n - 1)) end:
seq(a(n), n = 0..20);

PARI

a(n) = binomial(2*n, n) * binomial(2*n - 1, n); \\ Michel Marcus, Mar 28 2023

Formula

a(n) = (4 - 2 / n)^2 * a(n - 1) for n >= 2.

a(n) = A002894(n)/2 for n >= 1. - Peter Bala, Mar 28 2023