%I M1703 N0673 #50 Oct 21 2019 16:20:03

%S 1,1,2,6,36,240,1800,15120,141120,1693440,21772800,299376000,

%T 4390848000,68497228800,1133317785600,19833061248000,396661224960000,

%U 8299373322240000,181400588328960000,4135933413900288000,98228418580131840000,2426819753156198400000

%N Largest number in n-th row of triangle of Lah numbers (A008297 and A271703).

%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 Vincenzo Librandi, <a href="/A002868/b002868.txt">Table of n, a(n) for n = 0..100</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>

%F For 2 <= n <= 7, equals (n+1)!*n/2. - _Alexander R. Povolotsky_, Oct 16 2006

%p with(combinat): for n from 0 to 35 do big := 1: for m from 1 to n do if big < n!*binomial(n-1,m-1)/m! then big := n!*binomial(n-1,m-1)/m! fi: od: printf(`%d,`,big): od:

%t a[n_] := ( big = 1; For[ m = 1 , m <= n, m++, b = n!*Binomial[n - 1, m - 1]/m!; If[ big < b , big = b ]]; big); Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Sep 21 2012, after Maple *)

%o (Haskell)

%o a002868 n = if n == 0 then 1 else maximum $ map abs $ a008297_row n

%o -- _Reinhard Zumkeller_, Sep 30 2014

%Y Essentially the same as A001286.

%Y Cf. A000262, A008297, A105278, A271703.

%K nonn,nice,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Jan 03 2001