A274883 Triangle read by rows, T(n,k) = 2^k*binomial(n,k)*A057977(n-k) for n>=0 and 0<=k<=n.

1, 1, 2, 1, 4, 4, 3, 6, 12, 8, 2, 24, 24, 32, 16, 10, 20, 120, 80, 80, 32, 5, 120, 120, 480, 240, 192, 64, 35, 70, 840, 560, 1680, 672, 448, 128, 14, 560, 560, 4480, 2240, 5376, 1792, 1024, 256, 126, 252, 5040, 3360, 20160, 8064, 16128, 4608, 2304, 512

Offset: 0

Author

Peter Luschny, Jul 14 2016

Keywords

• nonn
• tabl

Examples

			Triangle starts:
                       1;
                      1, 2;
                    1, 4, 4;
                  3, 6, 12, 8;
               2, 24, 24, 32, 16;
            10, 20, 120, 80, 80, 32;
         5, 120, 120, 480, 240, 192, 64;
     35, 70, 840, 560, 1680, 672, 448, 128;
14, 560, 560, 4480, 2240, 5376, 1792, 1024, 256;
		

Crossrefs

Cf. A000079 (T(n,n)), A057977 (T(n,0)), A077587 (row sum).

Cf. A189912. Row reversed A091894 is a subtriangle.

Programs

Maple

T := (n,k) -> 2^k*binomial(n,k)*((n-k)!/floor((n-k)/2)!^2)/(floor((n-k)/2)+1);
seq(seq(T(n,k), k=0..n), n=0..9);