A114195 Riordan array (1/(1-3x),x(1-x)/(1-3x)^2).

1, 3, 1, 9, 8, 1, 27, 45, 13, 1, 81, 216, 106, 18, 1, 243, 945, 690, 192, 23, 1, 729, 3888, 3915, 1574, 303, 28, 1, 2187, 15309, 20223, 10941, 2993, 439, 33, 1, 6561, 58320, 97524, 67788, 24598, 5072, 600, 38, 1, 19683, 216513, 446148, 385560, 177498

Offset: 0

Author

Paul Barry, Nov 16 2005

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A082685. Diagonal sums are A114196.

Examples

			Triangle begins
1;
3, 1;
9, 8, 1;
27, 45, 13, 1;
81, 216, 106, 18, 1;
243, 945, 690, 192, 23, 1;
		

Formula

T(n, k)=sum{j=0..n, C(n, j)C(j+k, 2k)2^(j-k)}; T(n, k)=sum{j=0..n-k, C(k, j)C(n+k-j, 2k)(-1)^j*3^(n-k-j)}.

T(n,k) = 6*T(n-1,k) + T(n-1,k-1) - 9*T(n-2,k) - T(n-2,k-1), T(0,0) = T(1,1) = 1, T(1,0) = 3, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 18 2014