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A290443
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a(n) = Catalan(n)*Motzkin(n-1).
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2
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1, 2, 10, 56, 378, 2772, 21879, 181610, 1570426, 14024660, 128623768, 1206053576, 11523121900, 111885197400, 1101664016730, 10981102287240, 110647549986930, 1125688857747300, 11551507304378580, 119462291733779280, 1244159075360113380, 13040616137944154760, 137485676447508793950
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..23.
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FORMULA
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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
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MATHEMATICA
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motzkin[n_]:=Hypergeometric2F1[(1-n)/2, -n/2, 2, 4]; Table[CatalanNumber[n] motzkin[n - 1], {n, 50}] (* Indranil Ghosh, Aug 04 2017 *)
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CROSSREFS
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Cf. A000108, A001006, A151341, A290443.
Sequence in context: A000172 A097971 A191277 * A336961 A265954 A093303
Adjacent sequences: A290440 A290441 A290442 * A290444 A290445 A290446
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Aug 04 2017
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STATUS
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approved
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