A290443 a(n) = Catalan(n)*Motzkin(n-1).

1, 2, 10, 56, 378, 2772, 21879, 181610, 1570426, 14024660, 128623768, 1206053576, 11523121900, 111885197400, 1101664016730, 10981102287240, 110647549986930, 1125688857747300, 11551507304378580, 119462291733779280, 1244159075360113380, 13040616137944154760, 137485676447508793950

Offset: 1

Author

N. J. A. Sloane, Aug 04 2017

Keywords

• nonn

Crossrefs

Cf. A000108, A001006, A151341, A290443.

Programs

Mathematica

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

Formula

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