A358397 Number of pairs of partitions (A<=B, that is, A is a refinement of B) of [n] such that A is noncrossing and its nontrivial blocks are of type {a,b} with a <= n and b > n.

1, 1, 3, 9, 37, 157, 811, 4309, 26327, 164947, 1151477, 8224863, 64158567, 511177515, 4386520201, 38389960685, 358214414675, 3404632390971, 34234771676473, 350261221644771, 3768281045014927, 41210302324325919, 471585931164213345, 5480984322433817771, 66388136273738685321

Offset

0,3

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = Sum_{k=0..m} binomial(m,k)*binomial(m+e,k)*Bell(n-k), with m = floor(n/2), e = n mod 2 and where Bell(n) is the Bell exponential number A000110(n).

Crossrefs

Cf. A000110.

Sequence in context: A134818 A321737 A002751 * A245890 A119856 A077365

Adjacent sequences: A358394 A358395 A358396 * A358398 A358399 A358400

Keyword

nonn

Author

Francesca Aicardi, Nov 13 2022

Status

approved