A117316 Riordan array ((1-x)/(1-x-2x^2),x(1-x)/(1-x-2x^2)).

1, 0, 1, 2, 0, 1, 2, 4, 0, 1, 6, 4, 6, 0, 1, 10, 16, 6, 8, 0, 1, 22, 28, 30, 8, 10, 0, 1, 42, 72, 54, 48, 10, 12, 0, 1, 86, 148, 158, 88, 70, 12, 14, 0, 1, 170, 336, 342, 288, 130, 96, 14, 16, 0, 1, 342, 716, 846, 648, 470, 180, 126, 16, 18, 0, 1

Offset: 0

Author

Paul Barry, Mar 07 2006

Keywords

• easy
• nonn
• tabl

Comments

Product of A007318 and alternating sign version of A073370. Row sums are A001333. Diagonal sums are A052973. First column is A078008. Convolution array for A078008.

Examples

			Triangle begins
1,
0, 1,
2, 0, 1,
2, 4, 0, 1,
6, 4, 6, 0, 1,
10, 16, 6, 8, 0, 1,
22, 28, 30, 8, 10, 0, 1,
42, 72, 54, 48, 10, 12, 0, 1
		

Formula

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

T(n,k)=T(n-1,k)+T(n-1,k-1)+2*T(n-2,k)-T(n-2,k-1), T(0,0)= 1, T(1,0)=0, T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 04 2013