

A002871


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


2



1, 2, 4, 12, 48, 200, 1040, 5600, 33600, 222432, 1460928, 11487168, 84713728, 731574272, 6314147840, 55456727040, 548291597568, 5226494727168, 54361802626560, 586042688924160, 6149776714099200, 72895623466265600, 855187250563024896
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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. 167176. [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}] (* JeanFrançois Alcover, Feb 25 2015 *)


PROG

(PARI) a(n) = vecmax(vector(n+1, k, 2^(k1)*stirling(n, k1, 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



