A187442 A trisection of A001405 (central binomial coefficients): binomial(3*n,floor(3*n/2)), n >= 0.

1, 3, 20, 126, 924, 6435, 48620, 352716, 2704156, 20058300, 155117520, 1166803110, 9075135300, 68923264410, 538257874440, 4116715363800, 32247603683100, 247959266474052, 1946939425648112, 15033633249770520, 118264581564861424, 916312070471295267, 7219428434016265740

Offset

0,2

Comments

For the trisection of sequences see a comment and a reference under A187357.

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = binomial(3*n,floor(3*n/2)), n >= 0.

O.g.f.: G0(x^2) + 3*x*G2(x^2) with G0(x) and G2(x) the o.g.f.s of A187363 and A187365, respectively.

a(n) ~ 2^(3*n+1/2) / sqrt(3*Pi*n). - Amiram Eldar, Nov 16 2025

Mathematica

Table[Binomial[3n, Floor[(3n)/2]], {n, 0, 20}] (* Harvey P. Dale, Dec 23 2012 *)

Crossrefs

Cf. A187443 (binomial(3*n+1,floor((3*n+1)/2))), A187444 (binomial(3*n+2,floor((3*n+2)/2))/2).

Cf. A001405, A187357, A187363, A187365.

Sequence in context: A325890 A323563 A228750 * A167590 A228884 A138910

Adjacent sequences: A187439 A187440 A187441 * A187443 A187444 A187445

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 10 2011

Extensions

More terms from Amiram Eldar, Nov 16 2025

Status

approved