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# Sequence Notation Coorespondence

Sequences of "Sorting Numbers" in the OEIS
Sequence Motzkin's Notation
Partition numbers A000041$(n)=\displaystyle {!}^{!n}$ Bell numbers A000110$(n)=\displaystyle {!}^{n}$ Number of partitions of {1,...,n} A000262$(n)=\displaystyle {!}^{n+}$ Fubini numbers A000670$(n)=\displaystyle {\Sigma }_{>}^{n}$ E.g.f.: e^(2*(e^x - 1)) A001861$(n)=\displaystyle {!}^{{\underline {!}}\cdot n}$ Max_{k} { Number of partitions of n into k positive parts } A002569$(n)=\displaystyle {!\max }_{>}^{!n}$ n!*2^(n-1) A002866$(n)=\displaystyle {\Sigma }_{>}^{n+}$ (n+1)!*binomial(n,floor(n/2)) A002867$(n-1)=\displaystyle {\max }_{>}^{n+}$ Largest number in n-th row of triangle A008297 A002868$(n)=\displaystyle {!\max }_{>}^{n+}$ Largest number in n-th row of triangle A019538 A002869$(n)=\displaystyle {\max }_{>}^{n}$ Max_{k} Stirling2(n,k) A002870$(n)=\displaystyle {!\max }_{>}^{n}$ Max_{k} 2^k*Stirling2(n,k) A002871$(n)=\displaystyle {!\max }_{>}^{{\underline {!}}\cdot n}$ Column 2 of A162663 A002872$(n)=\displaystyle {!}^{{\underline {!}}2\cdot n}={!}^{{\underline {cy}}2\cdot n}$ "Sorting numbers" A002873$(n)=\displaystyle {!\max }_{>}^{{\underline {!}}2\cdot n}$ Column 3 of A162663 A002874$(n)=\displaystyle {!}^{{\underline {cy}}3\cdot n}$ "Sorting numbers" A002875$(n)=\displaystyle {!\max }_{>}^{{\underline {cy}}{3\cdot n}}$ Stirling numbers of the second kind A008277$(n,k)=\displaystyle {!k}_{>}^{n}$ Falling factorial A008279$(n,k)=\displaystyle {n}_{<}^{k}$ Number of partitions of n into k positive parts A008284$(n,k)=\displaystyle {!k}_{>}^{!n}$ k!*Stirling2(n,k) A019538$(n,k)=\displaystyle {k}_{>}^{n}$ Number of partitions of n into at most k positive parts A026820$(n,k)=\displaystyle {!k}^{!n}$ Column 5 of A162663 A036075$(n)=\displaystyle {!}^{{\underline {cy}}5\cdot n}$ Column 7 of A162663 A036077$(n)=\displaystyle {!}^{{\underline {cy}}7\cdot n}$ Column 11 of A162663 A036081$(n)=\displaystyle {!}^{{\underline {cy}}11\cdot n}$ Sum_{i<=k} Stirling2(n,i) A102661$(n,k)=\displaystyle {!k}^{n}$ Column 13 of A162663 A141009$(n)=\displaystyle {!}^{{\underline {cy}}13\cdot n}$ n!*binomial(n-1,k-1) A156992$(n,k)=\displaystyle {k}_{>}^{n+}$ 