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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.
0
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
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
KEYWORD
nonn
AUTHOR
Francesca Aicardi, Nov 13 2022
STATUS
approved