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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

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OFFSET

0,3

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.

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]

EXAMPLE

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.