A084417 Triangle read by rows: T(n,k)=sum((n+1-i)!*stirling2(n,n+1-i),i=1..k), n>=1, 1<=k<=n.

1, 2, 3, 6, 12, 13, 24, 60, 74, 75, 120, 360, 510, 540, 541, 720, 2520, 4080, 4620, 4682, 4683, 5040, 20160, 36960, 45360, 47166, 47292, 47293, 40320, 181440, 372960, 498960, 539784, 545580, 545834, 545835, 362880, 1814400, 4142880, 6048000

Offset: 1

Author

N. J. A. Sloane, Jun 24 2003

Keywords

• nonn
• tabl
• easy

Comments

Interpolates between A000670 and factorials.

Examples

			1;2,3;6,12,13;24,60,74,75;120,360,510,540,541;
		

Crossrefs

Mirror image of array in A084416.

T(n, 1)=n!=A000142(n), T(n, n)=A000670(n), T(n, n-1)=A052875(n).

Programs

Maple

with(combinat): T:=(n,k)->sum((n+1-i)!*stirling2(n,n+1-i),i=1..k): seq(seq(T(n,k),k=1..n),n=1..10);

Formula

T(n, k)=sum((n+1-i)!*stirling2(n, n+1-i), i=1..k), n>=1, 1<=k<=n.

Extensions

Edited by Emeric Deutsch, May 11 2004