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A155581 a(n)=If[IntegerQ[((6*n - 4)/( n + 1))*a(n - 1)], ((6*n - 4)/(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, 7, 28, 84, 384, 1824, 6080, 30400, 304000, 1064000, 12768000, 67488000, 359936000, 1934656000, 30954496000, 526226432000, 2880397312000, 15842185216000, 316843704320000, 1757042360320000, 38654931927040000 (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 higher).

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n)=If[IntegerQ[((6*n - 4)/( n + 1))*a(n - 1)], ((6*n - 4)/(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[((6*n - 4)/(n + 1))*a[n - 1]], ((3*n - 2)/(n + 1))* a[n - 1],

If[IntegerQ[((6*n - 4)/(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: A099815 A123363 A102961 * A048504 A092465 A099488

Adjacent sequences:  A155578 A155579 A155580 * A155582 A155583 A155584

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Jan 24 2009

STATUS

approved

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Last modified March 19 13:37 EDT 2019. Contains 321330 sequences. (Running on oeis4.)