Sequence
|
Motzkin's Notation
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Partition numbers
|
A000041
|
Bell numbers
|
A000110
|
Number of partitions of {1,...,n}
|
A000262
|
Fubini numbers
|
A000670
|
E.g.f.: e^(2*(e^x - 1))
|
A001861
|
Max_{k} { Number of partitions of n into k positive parts }
|
A002569
|
n!*2^(n-1)
|
A002866
|
(n+1)!*binomial(n,floor(n/2))
|
A002867
|
Largest number in n-th row of triangle A008297
|
A002868
|
Largest number in n-th row of triangle A019538
|
A002869
|
Max_{k} Stirling2(n,k)
|
A002870
|
Max_{k} 2^k*Stirling2(n,k)
|
A002871
|
Column 2 of A162663
|
A002872
|
Max_{k} #{partitions of 2n into k parts which are invariant under (12)(34)...(2n-1,2n)}
|
A002873
|
Column 3 of A162663
|
A002874
|
?
|
A002875
|
Stirling numbers of the second kind
|
A008277
|
Falling factorial
|
A008279
|
Number of partitions of n into k positive parts
|
A008284
|
k!*Stirling2(n,k)
|
A019538
|
Number of partitions of n into at most k positive parts
|
A026820
|
Column 5 of A162663
|
A036075
|
Column 7 of A162663
|
A036077
|
Column 11 of A162663
|
A036081
|
Sum_{i<=k} Stirling2(n,i)
|
A102661
|
Column 13 of A162663
|
A141009
|
n!*binomial(n-1,k-1)
|
A156992
|