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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
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).
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
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, Jan 24 2009
STATUS
approved