A130471 First differences of antidiagonal sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.

0, 2, 5, 21, 106, 640, 4527, 36539, 331508, 3338358, 36946489, 445724977, 5821580670, 81839381996, 1232102291651, 19778348559015, 337223021210632, 6086161135368034, 115915940643233613, 2323409451689985053

Offset: 1

Author

Klaus Brockhaus, May 28 2007

Keywords

• nonn

Comments

a(n) = A130470(n+1) - A130470(n).

Examples

			a(7) = A130470(8) - A130470(7) = 5302 - 775 = 4527.
		

Crossrefs

Cf. A130469 (T read by rows), A129867 (row sums), A130470 (antidiagonal sums).

Programs

Magma

m:=21; T:=[ [ k*Factorial(j-k): k in [1..j-1] ] cat [ 1 ]: j in [1..m] ]; S:=[ &+[ T[j-k+1][k]: k in [1..(j+1) div 2] ]: j in [1..m] ]; [ S[j+1]-S[j]: j in [1..m-1] ];