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%I M1261 N0483 #51 Jun 06 2017 17:01:56
%S 1,2,4,12,48,200,1040,5600,33600,222432,1460928,11487168,84713728,
%T 731574272,6314147840,55456727040,548291597568,5226494727168,
%U 54361802626560,586042688924160,6149776714099200,72895623466265600,855187250563024896
%N a(n) = max_{k=0..n} 2^k*A048993(n,k)
%C Original name: Sorting numbers (see Motzkin article for details).
%C For n>0, a(n) is also the maximum term in row n of the triangle in A227450. - _Danny Rorabaugh_, Oct 24 2015
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Alois P. Heinz, <a href="/A002871/b002871.txt">Table of n, a(n) for n = 0..250</a>
%H Victor Meally, <a href="/A002868/a002868.pdf">Comparison of several sequences given in Motzkin's paper "Sorting numbers for cylinders...", letter to N. J. A. Sloane, N. D.</a>
%H T. S. Motzkin, <a href="/A000262/a000262.pdf">Sorting numbers for cylinders and other classification numbers</a>, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176. [Annotated, scanned copy]
%H OEIS Wiki, <a href="http://oeis.org/wiki/Sorting_numbers">Sorting numbers</a>
%H <a href="/index/So#sorting">Index entries for sequences related to sorting</a>
%F a(n) = max{2^k*stirling2(n,k), k=0..n}. - _Sean A. Irvine_, Mar 26 2013
%p a:= n-> max(seq(2^k*Stirling2(n, k), k=0..n)):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Mar 26 2013
%t a[n_] := Max[Table[2^k*StirlingS2[n, k], {k, 0, n}]]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Feb 25 2015 *)
%o (PARI) a(n) = vecmax(vector(n+1, k, 2^(k-1)*stirling(n, k-1, 2))); \\ _Michel Marcus_, Feb 25 2015
%Y Cf. A008277, A048993, A227450.
%K nonn,nice
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Sean A. Irvine_, Mar 26 2013
%E New name from _Danny Rorabaugh_, Oct 24 2015
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