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)]]

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).

Links

Table of n, a(n) for n=0..25.

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

A000108

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