

A033552


Number of partitions into Catalan numbers.


4



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

R. 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(mc,k,c) + f(m,k+1,2*c*(2*k+1)/(k+2)). [Reinhard Zumkeller, Apr 09 2010]


CROSSREFS

Cf. A000108.
Cf. A176137. [Reinhard Zumkeller, Apr 09 2010]
Sequence in context: A274165 A011874 A000115 * A062420 A089197 A017874
Adjacent sequences: A033549 A033550 A033551 * A033553 A033554 A033555


KEYWORD

easy,nonn


AUTHOR

Marc LeBrun


STATUS

approved



