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%I #14 May 11 2013 11:01:15
%S 1,2,5,6,14,21,24,54,80,105,120,264,390,512,633,720,1560,2304,3030,
%T 3752,4473,5040,10800,15960,21024,26070,31112,36153,40320,85680,
%U 126720,167160,207504,247830,288152,328473,362880,766080,1134000
%N Array read by antidiagonals: T(m,n) = m*(m+n-1)! + Sum( n <= i <= m+n-2 ) i!
%C Index numbers (compare A055089) of transpositions.
%H Tilman Piesk, <a href="/A211369/b211369.txt">Table of n, a(n) for n = 1..2016</a>
%H Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Inversion_%28discrete_mathematics%29#arrays3">Arrays of permutations</a> (Wikiversity)
%F T(m,1) = A001563(m) + A007489(m-1). - _R. J. Mathar_, May 11 2013
%e T(3,2) = 3*4! + Sum( 2 <= i <= 3 ) i!
%e = 3*4! + 2! + 3!
%e = 3*24 + 2 + 6 = 80.
%e The array starts:
%e 1, 2, 6, 24, 120,...
%e 5, 14, 54, 264, 1560,...
%e 21, 80, 390, 2304, 15960,...
%e 105, 512, 3030, 21024,167160,...
%e 633, 3752, 26070,207504,1860600,...
%p A211369 := proc(m,n)
%p m*(m+n-1)!+add(i!,i=n..m+n-2) ;
%p end proc: # _R. J. Mathar_, May 10 2013
%Y Cf. A055089, A000142 (row 1), A052649 (row 2)
%K nonn,tabl
%O 1,2
%A _Tilman Piesk_, Jul 07 2012