A211369 - OEIS

%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