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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

%I

%S 1,1,2,5,10,30,180,585,1430,3575,9100,31850,83300,220150,792540,

%T 11888100,32167800,87567900,1576222200,4334611050,11971782900,

%U 33194488950,92367273600,257858638800,722004188640,18050104716000

%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)]]

%C Catalan recursion is:

%C a[0] = 1; a[n_] := a[n] = ((4*n - 2)/(n + 1))*a[n - 1];

%C The object here is to get a sequence that is Catalan like, but lower ( bifurcates lower).

%F a(n)=If[IntegerQ[((3*n - 2)/( n + 1))*a(n - 1)], ((3*n - 2)/(n + 1))* a(n - 1),

%F If[IntegerQ[((4*n - 2)/(n + 1))*a( n - 1)], ((4*n - 2)/(n + 1))*a(n - 1), n*a(n - 1)]]

%t Clear [a, n]; a[0] = 1;

%t a[n_] := a[n] = If[IntegerQ[((3*n - 2)/(n + 1))*a[n - 1]], ((3*n - 2)/(n + 1))* a[n - 1],

%t If[IntegerQ[((4*n - 2)/(n + 1))*a[n - 1]], ((4*n - 2)/(n + 1))*a[n - 1], n*a[n - 1]]];

%t Table[a[n], {n, 0, 30}]

%Y A000108

%K nonn,uned

%O 0,3

%A _Roger L. Bagula_, Jan 24 2009

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Last modified June 19 03:31 EDT 2021. Contains 345125 sequences. (Running on oeis4.)