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 A155580 a(n)=If[IntegerQ[((3*n - 2)/( n + 1))*a(n - 1)], ((3*n - 2)/(n + 1))* a(n - 1), If[IntegerQ[((4*n - 2)/(n + 1))*a( n - 1)], ((4*n - 2)/(n + 1))*a(n - 1), n*a(n - 1)]] 0
 1, 1, 2, 5, 10, 30, 180, 585, 1430, 3575, 9100, 31850, 83300, 220150, 792540, 11888100, 32167800, 87567900, 1576222200, 4334611050, 11971782900, 33194488950, 92367273600, 257858638800, 722004188640, 18050104716000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Catalan recursion is: a[0] = 1; a[n_] := a[n] = ((4*n - 2)/(n + 1))*a[n - 1]; The object here is to get a sequence that is Catalan like, but lower ( bifurcates lower). LINKS FORMULA a(n)=If[IntegerQ[((3*n - 2)/( n + 1))*a(n - 1)], ((3*n - 2)/(n + 1))* a(n - 1), If[IntegerQ[((4*n - 2)/(n + 1))*a( n - 1)], ((4*n - 2)/(n + 1))*a(n - 1), n*a(n - 1)]] MATHEMATICA Clear [a, n]; a[0] = 1; a[n_] := a[n] = If[IntegerQ[((3*n - 2)/(n + 1))*a[n - 1]], ((3*n - 2)/(n + 1))* a[n - 1], If[IntegerQ[((4*n - 2)/(n + 1))*a[n - 1]], ((4*n - 2)/(n + 1))*a[n - 1], n*a[n - 1]]]; Table[a[n], {n, 0, 30}] CROSSREFS Sequence in context: A047113 A239630 A239629 * A226963 A018386 A270521 Adjacent sequences:  A155577 A155578 A155579 * A155581 A155582 A155583 KEYWORD nonn,uned AUTHOR Roger L. Bagula, Jan 24 2009 STATUS approved

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)