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A033552 Number of partitions into Catalan numbers. 4


%S 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,

%T 58,62,68,73,80,85,92,98,106,113,121,128,137,145,155,163,175,184,197,

%U 207,220,232,246,259,274,287,304,318,336,351,371,388,409,427,449,469

%N Number of partitions into Catalan numbers.

%H R. Zumkeller, <a href="/A033552/b033552.txt">Table of n, a(n) for n = 0..250</a>

%H Igor Pak, <a href="https://arxiv.org/abs/1803.06636">Complexity problems in enumerative combinatorics</a>, arXiv:1803.06636 [math.CO], 2018.

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

%F 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]

%Y Cf. A000108.

%Y Cf. A176137. [_Reinhard Zumkeller_, Apr 09 2010]

%K easy,nonn

%O 0,3

%A _Marc LeBrun_

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Last modified January 20 16:38 EST 2019. Contains 319335 sequences. (Running on oeis4.)