A100033 Bisection of A001700.

3, 35, 462, 6435, 92378, 1352078, 20058300, 300540195, 4537567650, 68923264410, 1052049481860, 16123801841550, 247959266474052, 3824345300380220, 59132290782430712, 916312070471295267, 14226520737620288370, 221256270138418389602, 3446310324346630677300, 53753604366668088230810

Offset

0,1

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = binomial(4*n+3, 2*n+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: (Start)

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)

a(n) ~ 2^(4*n+5/2) / sqrt(Pi*n). - Amiram Eldar, Sep 20 2025

Maple

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

Mathematica

a[n_] := Binomial[4*n+3, 2*n+2]; Array[a, 20, 0] (* Amiram Eldar, Sep 20 2025 *)

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

More terms from Amiram Eldar, Sep 20 2025

Status

approved