A033552 Number of partitions into Catalan numbers.

1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 17, 19, 22, 24, 27, 30, 34, 37, 41, 44, 49, 53, 58, 62, 68, 73, 80, 85, 92, 98, 106, 113, 121, 128, 137, 145, 155, 163, 175, 184, 197, 207, 220, 232, 246, 259, 274, 287, 304, 318, 336, 351, 371, 388, 409, 427, 449, 469

Offset: 0

Author

Marc LeBrun

Keywords

• easy
• nonn

Examples

			n=4 has 3 partitions: 2+2, 2+1+1, 1+1+1+1.
n=5 has 4 partitions: 5, 2+2+1, 2+1+1+1, 1+1+1+1+1.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..250
• Igor Pak, Complexity problems in enumerative combinatorics, arXiv:1803.06636 [math.CO], 2018.

Crossrefs

Cf. A000108.

Cf. A176137. [Reinhard Zumkeller, Apr 09 2010]

Formula

G.f.: Product_{n>=1} 1/(1 - x^(binomial(2*n, n)/(n+1))).

a(n) = f(n,1,1) with f(m,k,c) = if c > m then 0^m else f(m-c,k,c) + f(m,k+1,2*c*(2*k+1)/(k+2)). [Reinhard Zumkeller, Apr 09 2010]