A211369 Array read by antidiagonals: T(m,n) = m*(m+n-1)! + Sum( n <= i <= m+n-2 ) i!

1, 2, 5, 6, 14, 21, 24, 54, 80, 105, 120, 264, 390, 512, 633, 720, 1560, 2304, 3030, 3752, 4473, 5040, 10800, 15960, 21024, 26070, 31112, 36153, 40320, 85680, 126720, 167160, 207504, 247830, 288152, 328473, 362880, 766080, 1134000

Offset

1,2

Comments

Index numbers (compare A055089) of transpositions.

Links

Tilman Piesk, Table of n, a(n) for n = 1..2016

Tilman Piesk, Arrays of permutations (Wikiversity)

Formula

T(m,1) = A001563(m) + A007489(m-1). - R. J. Mathar, May 11 2013

Example

T(3,2) = 3*4! + Sum( 2 <= i <= 3 ) i!
= 3*4! + 2! + 3!
= 3*24 + 2 + 6 = 80.
The array starts:
     1,     2,     6,    24,   120,...
     5,    14,    54,   264,  1560,...
    21,    80,   390,  2304, 15960,...
   105,   512,  3030, 21024,167160,...
   633,  3752, 26070,207504,1860600,...

Maple

A211369 := proc(m, n)
    m*(m+n-1)!+add(i!, i=n..m+n-2) ;
end proc: # R. J. Mathar, May 10 2013

Crossrefs

Cf. A055089, A000142 (row 1), A052649 (row 2)

Sequence in context: A191229 A191120 A245540 * A006596 A000092 A100630

Adjacent sequences: A211366 A211367 A211368 * A211370 A211371 A211372

Keyword

nonn,tabl

Author

Tilman Piesk, Jul 07 2012

Status

approved