A002871 a(n) = max_{k=0..n} 2^k*A048993(n,k).

1, 2, 4, 12, 48, 200, 1040, 5600, 33600, 222432, 1460928, 11487168, 84713728, 731574272, 6314147840, 55456727040, 548291597568, 5226494727168, 54361802626560, 586042688924160, 6149776714099200, 72895623466265600, 855187250563024896

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

Original name: Sorting numbers (see Motzkin article for details).

For n>0, a(n) is also the maximum term in row n of the triangle in A227450. - Danny Rorabaugh, Oct 24 2015

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250
• Victor Meally, Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.
• T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
• OEIS Wiki, Sorting numbers
• Index entries for sequences related to sorting

Crossrefs

Cf. A008277, A048993, A227450.

Programs

Maple

a:= n-> max(seq(2^k*Stirling2(n, k), k=0..n)):
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 26 2013

Mathematica

a[n_] := Max[Table[2^k*StirlingS2[n, k], {k, 0, n}]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 25 2015 *)

PARI

a(n) = vecmax(vector(n+1, k, 2^(k-1)*stirling(n, k-1, 2))); \\ Michel Marcus, Feb 25 2015

Formula

a(n) = max{2^k*Stirling2(n,k), k=0..n}. - Sean A. Irvine, Mar 26 2013

Extensions

More terms from Sean A. Irvine, Mar 26 2013

New name from Danny Rorabaugh, Oct 24 2015