A100630 - OEIS

%I #13 Jul 13 2012 17:31:39

%S 1,2,5,6,14,23,24,54,86,119,120,264,414,566,719,720,1560,2424,3294,

%T 4166,5039,5040,10800,16680,22584,28494,34406,40319,40320,85680,

%U 131760,177960,224184,270414,316646,362879,362880,766080,1174320,1583280

%N Array read by antidiagonals: T(m,n) = Sum(1<=i<=m) [ i*(n-1+i)! ]

%C Inversion vector corresponding to T(m,n): ( n zeros , 1,2,3,...,m , zeros... )

%C These are the numbers of permutations (in reverse colexicographical order, compare A055089) that reverse a set of consecutive elements and leave all other elements unchanged. Permutation A(m,n) reverses all elements from n to m+n.

%C The former title of this sequence refers to finite tables of permutations in lexicographical order: "Triangle read by rows: row n gives the index number in the tables of permutations of order n+1, n+2, ... of the permutation in which the first n items are reversed and the remaining items are in order."

%H Tilman Piesk, <a href="/A100630/b100630.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">Inversion (discrete mathematics)</a> (Wikiversity)

%e T(3,2) = Sum( 1 <= i <= 3 ) [ i * (1+i)! ]

%e = 1*(1+1)! + 2*(1+2)! + 3*(1+3)!

%e = 1*2 + 2*6 + 3*24

%e = 86

%o MATLAB code is shown on the Wikiversity page.

%o Using Iverson's J language, A. p for a permutation p gives the row number in the table of permutations of order (length of p) which has p as its value. For example, q 0 4 9 6 7 5 1 11 8 10 2 3 A. q 13610272.

%Y See A100711 for another version. Row 2 is A052649.

%K easy,nonn,tabl

%O 1,2

%A Eugene McDonnell (eemcd(AT)mac.com), Dec 03 2004

%E Rewritten by _Tilman Piesk_, Jul 13 2012