A120493 Triangle T(n,k) read by rows ; multiply row n of Pascal's triangle (A007318) by A024175(n).

1, 1, 1, 2, 4, 2, 5, 15, 15, 5, 14, 56, 84, 56, 14, 42, 210, 420, 420, 210, 42, 132, 792, 1980, 2640, 1980, 792, 132, 428, 2996, 8988, 14980, 14980, 8988, 2996, 428, 1416, 11328, 39648, 79296, 99120, 79296, 39648, 11328, 1416

Offset: 0

Author

Philippe Deléham, Aug 05 2006

Keywords

• nonn
• tabl

Comments

Triangle given by [1, 1, 1, 1, 1, 1, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 0, 0, 0, ...] where DELTA is the operator defined in A084938.

Examples

			Triangle begins:
1;
1, 1;
2, 4, 2;
5, 15, 15, 5;
14, 56, 84, 56, 14;
42, 210, 420, 420, 210, 42;
132, 792, 1980, 2640, 1980, 792, 132;
428, 2996, 8988, 14980, 14980, 8988, 2996, 428;
1416, 11328, 39648, 79296, 99120, 79296, 39648, 11328, 1416 ;...
		

Formula

T(n,k)=A007318(n,k)*A024175(n).

T(n,k)=6*T(n-1,k)+6*T(n-1,k-1)-10*T(n-2,k)-20*T(n-2,k-1)-10*T(n-2,k-2)+4*T(n-3,k)+12*T(n-3,k-1)+12*T(n-3,k-2)+4*T(n-3,k-3) for n>3, T(0,0)=T(1,0)=T(1,1)=1, T(2,0)=T(2,2)=2, T(2,1)=4, T(3,0)=T(3,3)=5, T(3,1)=T(3,2)=15, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Nov 22 2013

G.f.: (-1 +5*x +5*x*y -6*x^2 -12*x^2*y -6*x^2*y^2 +x^3 +3*x^3*y +3*x^3*y^2 +x^3*y^3)/( (-1+2*x+2*x*y) *(2*x^2*y^2+4*x^2*y+2*x^2-4*x*y-4*x+1) ). - R. J. Mathar, Aug 12 2015