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

0,3

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(m-c,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: A011874 A000115 A367253 * A062420 A089197 A017874

Adjacent sequences: A033549 A033550 A033551 * A033553 A033554 A033555

Keyword

easy,nonn

Author

Marc LeBrun

Status

approved