A130470 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.

1, 1, 3, 8, 29, 135, 775, 5302, 41841, 373349, 3711707, 40658196, 486383173, 6307963843, 88147345839, 1320249637490, 21098598196505, 358321619407137, 6444482754775171, 122360423398008784, 2445769875087993837

Offset: 1

Author

Klaus Brockhaus, May 28 2007

Keywords

• nonn

Examples

			Antidiagonal starting at T(7,1) is 720, 48, 6, 1, so a(7) = 775.
		

Crossrefs

Cf. A130469 (T read by rows), A129867 (row sums of T), A130471 (first differences).

Programs

Magma

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