A100033 Bisection of A001700.

3, 35, 462, 6435, 92378, 1352078, 20058300, 300540195, 4537567650, 68923264410, 1052049481860, 16123801841550, 247959266474052, 3824345300380220, 59132290782430712, 916312070471295267, 14226520737620288370

Offset

0,1

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = binomial(4n+3, 2n+2). - Emeric Deutsch, Dec 09 2004

From Peter Bala, Mar 19 2023: (Start)

a(n) = (1/2)*Sum_{k = 0..2*n+2} binomial(2*n+2,k)^2.

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

a(n) = 2*(4*n + 1)*(4*n + 3)/((n + 1)*(2*n + 1)) * a(n-1). (End)

From Peter Bala, Mar 28 2023

a(n) = (1/(2*n + 2))*Sum_{k = 0..2*n+2} k*binomial(2*n+2,k)^2.

a(n) = 2*(n + 1)*hypergeom([-1 - 2*n, -1 - 2*n], [2], 1). (End)

Maple

a:=n->binomial(4*n+3, 2*n+2): seq(a(n), n=0..19);

Crossrefs

Cf. A001700, A002458, A187364, A187365.

Sequence in context: A065929 A161495 A179135 * A259557 A184554 A046032

Adjacent sequences: A100030 A100031 A100032 * A100034 A100035 A100036

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 20 2004

Extensions

More terms from Emeric Deutsch, Dec 09 2004

Status

approved