A048743 Triangle a(n,k) = k!*C(n-1,k-1)*Stirling_2(n,k), 1<=k<=n.

1, 1, 2, 1, 12, 6, 1, 42, 108, 24, 1, 120, 900, 960, 120, 1, 310, 5400, 15600, 9000, 720, 1, 756, 27090, 168000, 252000, 90720, 5040, 1, 1778, 121716, 1428840, 4410000, 4021920, 987840, 40320, 1, 4080, 508200, 10442880, 58388400, 106686720

Offset: 1

Author

Alford Arnold

Keywords

• easy
• nonn
• tabl

Examples

			The 3rd row is formed from [ 1,2,6,24 ]*[ 1,3,3,1 ]*[ 1,7,6,1 ] => [ 1,42,108,24 ].
1;
1,2;
1,12,6;
1,42,108,24;
1,120,900,960,120;
		

Crossrefs

Cf. A007318, A008277. Row sums give A045531.

Programs

Maple

A048743 := proc(n,k) k!*binomial(n-1,k-1)*combinat[stirling2](n,k) ; end proc:
seq(seq(A048743(n,k),k=1..n),n=1..12) ; # R. J. Mathar, Aug 30 2011

Mathematica

Flatten[Table[k!Binomial[n-1,k-1]StirlingS2[n,k],{n,10},{k,n}]] (* Harvey P. Dale, Feb 21 2013 *)

Extensions

More terms from James Sellers, Apr 22 2000