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 A002874 Sorting numbers. (Formerly M1863 N0738) 12

%I M1863 N0738

%S 1,2,8,42,268,1994,16852,158778,1644732,18532810,225256740,2933174842,

%T 40687193548,598352302474,9290859275060,151779798262202,

%U 2600663778494172,46609915810749130,871645673599372868

%N Sorting numbers.

%C Equals column 3 of A162663. [_Michel Marcus_, Mar 27 2013]

%D T. S. Motzkin, Sorting numbers ...: for a link to this paper see A000262.

%D T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176.

%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 T. D. Noe, <a href="/A002874/b002874.txt">Table of n, a(n) for n=0..100</a>

%H <a href="/index/So#sorting">Index entries for sequences related to sorting</a>

%F E.g.f.: exp (( exp(3*x) - 4) / 3 + exp(x) ).

%t u[0,j_]:=1;u[k_,j_]:=u[k,j]=Sum[Binomial[k-1,i-1]Plus@@(u[k-i,j]#^(i-1)&/@Divisors[j]),{i,k}]; Table[u[n,3],{n,0,12}] (* _Wouter Meeussen_, Dec 06 2008 *)

%t mx = 16; p = 3; Range[0, mx]! CoefficientList[ Series[ Exp[ (Exp[p*x] - p - 1)/p + Exp[x]], {x, 0, mx}], x] (* _Robert G. Wilson v_, Dec 12 2012 *)

%Y u[n,j] generates for j=1, A000110 Bell numbers; j=2, A002872 "Sorting numbers"; j=3, A002874 "Sorting numbers"; j=4, A141003 (Mathar); j=5, A036075 "Sorting numbers"; j=6, A141004 (Mathar); j=7, A036077 "Sorting numbers" [From _Wouter Meeussen_, Dec 06 2008]

%K nonn,easy,nice

%O 0,2

%A _N. J. A. Sloane_, _Simon Plouffe_

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