A290442 a(n) = Catalan(n-1)*Motzkin(n).

1, 2, 8, 45, 294, 2142, 16764, 138567, 1194050, 10638056, 97383208, 911829646, 8702182020, 84418698600, 830606179680, 8274230277615, 83330214144930, 847407871749780, 8692682350690800, 89868901315880610, 935699342853054780, 9805180025713805460, 103353379063190310600, 1095295964528435629050

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Formula

n*(n+2)*a(n) -2*(2*n+1)*(2*n-3)*a(n-1) -12*(2*n-3)*(2*n-5)*a(n-2) =0. - R. J. Mathar, Aug 05 2017

Mathematica

motzkin[n_]:=Hypergeometric2F1[(1-n)/2, -n/2, 2, 4]; Table[CatalanNumber[n - 1] motzkin[n], {n, 50}] (* Indranil Ghosh, Aug 04 2017 *)

Crossrefs

Cf. A000108, A001006, A151341, A290443.

Sequence in context: A139015 A197996 A258622 * A316367 A308599 A367316

Adjacent sequences: A290439 A290440 A290441 * A290443 A290444 A290445

Keyword

nonn

Author

N. J. A. Sloane, Aug 04 2017

Status

approved