A130469 Triangular array read by rows: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.

1, 1, 1, 2, 2, 1, 6, 4, 3, 1, 24, 12, 6, 4, 1, 120, 48, 18, 8, 5, 1, 720, 240, 72, 24, 10, 6, 1, 5040, 1440, 360, 96, 30, 12, 7, 1, 40320, 10080, 2160, 480, 120, 36, 14, 8, 1, 362880, 80640, 15120, 2880, 600, 144, 42, 16, 9, 1, 3628800, 725760, 120960, 20160, 3600

Offset: 1

Author

Klaus Brockhaus, May 28 2007

Keywords

• nonn
• tabl

Comments

T is also defined in A129867, which gives row sums of T.

Examples

			First seven rows of T are
[ 1 ]
[ 1, 1 ]
[ 2, 2, 1 ]
[ 6, 4, 3, 1 ]
[ 24, 12, 6, 4, 1 ]
[ 120, 48, 18, 8, 5, 1 ]
[ 720, 240, 72, 24, 10, 6, 1 ]
		

Crossrefs

Cf. A129867, A130470 (antidiagonal sums), A130471 (first differences of antidiagonal sums).

Programs

Magma

m:=11; &cat[ [ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]: j in [1..m] ];