A379099 a(n) = Sum_{k=0..n} binomial(2*k, k)*binomial(2*n, n)/(n + 1). Row sums of A379100.

1, 3, 18, 145, 1386, 14742, 168300, 2019303, 25135110, 321849814, 4215006588, 56222048610, 761436454492, 10446021648900, 144895117640040, 2029085114629545, 28652994844093170, 407600869429602090, 5836323240704117700, 84058779645184757490, 1217059539049881032220

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = CatalanNumber(n)*binomial(2*n, n)*hypergeom([1, -n], [1/2 - n], 1/4).

a(n) = A000108(n) * A006134(n).

Maple

CatalanNumber := n -> binomial(2*n, n)/(n + 1):
a := n -> CatalanNumber(n)*binomial(2*n, n)*hypergeom([1, -n], [1/2 - n], 1/4):
seq(simplify(a(n)), n = 0..20);

Crossrefs

Cf. A000108, A000984, A006134, A379100.

Sequence in context: A289428 A123308 A374864 * A177383 A074525 A118331

Adjacent sequences: A379090 A379091 A379092 * A379100 A379101 A379103

Keyword

nonn,new

Author

Peter Luschny, Dec 15 2024

Status

approved