A128413 Inverse of number triangle A128412.

1, 2, 1, 12, 8, 1, 80, 60, 12, 1, 560, 448, 112, 16, 1, 4032, 3360, 960, 180, 20, 1, 29568, 25344, 7920, 1760, 264, 24, 1, 219648, 192192, 64064, 16016, 2912, 364, 28, 1, 1647360, 1464320, 512512, 139776, 29120, 4480, 480, 32, 1, 12446720

Offset: 0

Author

Paul Barry, Mar 02 2007

Keywords

• easy
• nonn
• tabl

Comments

First column is A069723.

Examples

			Triangle begins
1,
2, 1,
12, 8, 1,
80, 60, 12, 1,
560, 448, 112, 16, 1,
4032, 3360, 960, 180, 20, 1,
29568, 25344, 7920, 1760, 264, 24, 1,
219648, 192192, 64064, 16016, 2912, 364, 28, 1
		

Crossrefs

Cf. A128417.

Formula

Number triangle T(n,k)=if(k=0,2^n*(C(2n,n)/2+0^n/2),2^(n-k)*C(2n,n-k)); Column k has g.f. if(k=0,4x/(sqrt(1-8x)(1-sqrt(1-8x))),(1/sqrt(1-8x))*((1-4x-sqrt(1-8x))/(8x))^k);