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: A123308 A374864 A381915 * A177383 A074525 A118331

Adjacent sequences: A379096 A379097 A379098 * A379100 A379101 A379102

Keyword

nonn

Author

Peter Luschny, Dec 15 2024

Status

approved