A273399 a(n) = Catalan(Catalan(n)).

1, 1, 2, 42, 2674440, 39044429911904443959240, 10934377152170553993439479038404269881062854488806451985760537780703486068308

Offset: 0

Author

Waldemar Puszkarz, May 21 2016

Keywords

• nonn
• easy

Comments

Next term, a(7), which has 255 digits and is equal to Catalan(429), is too large to include.

The number of digits of a(n) grows faster than Fibonacci(n) or Catalan(n-1), but slower than Catalan(n).

Examples

			a(3) = Catalan(Catalan(3)) = Catalan(5) = 42.
		

Crossrefs

Cf. A000108 (Catalan), A273400 (related sequence).

Programs

Maple

a:= ((n-> binomial(2*n, n)/(n+1))@@2):
seq(a(n), n=0..7);  # Alois P. Heinz, Jun 12 2016

Mathematica

CatalanNumber[CatalanNumber[Range[0,6]]]
Table[CatalanNumber[CatalanNumber[n]], {n, 0,6}]

PARI

for(n=0,6, cn=binomial(2*n, n)/(n+1); cn2=binomial(2*cn, cn)/(cn+1); print1(cn2 ","))

Formula

a(n) = A000108(A000108(n)).