A002871 a(n) = max_{k=0..n} 2^k*A048993(n,k). (Formerly M1261 N0483)

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

Offset

0,2

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A008277, A048993, A227450.

Sequence in context: A277281 A172452 A004527 * A013172 A321009 A052849

Adjacent sequences: A002868 A002869 A002870 * A002872 A002873 A002874

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Mar 26 2013

New name from Danny Rorabaugh, Oct 24 2015

Status

approved