A103316 Riordan array (1/(1+2x), x/(1+x)).

1, -2, 1, 4, -3, 1, -8, 7, -4, 1, 16, -15, 11, -5, 1, -32, 31, -26, 16, -6, 1, 64, -63, 57, -42, 22, -7, 1, -128, 127, -120, 99, -64, 29, -8, 1, 256, -255, 247, -219, 163, -93, 37, -9, 1, -512, 511, -502, 466, -382, 256, -130, 46, -10, 1, 1024, -1023, 1013, -968, 848, -638, 386, -176, 56, -11, 1, -2048, 2047, -2036, 1981

Offset: 0

Author

Paul Barry, Jan 30 2005

Keywords

• easy
• sign
• tabl

Comments

Inverse array of A029653. Signed version of A055248. Row sums are (-1)^n*A011782(n), with g.f. (1+x)/(1+2x). Diagonal sums are (-1)^n*A027934(n), with g.f. (1+x)/((1+2x)(1+x-x^2)).

Examples

			Rows start {1}, {-2,1}, {4,-3,1}, {-8,7,-4,1},...
		

Formula

Number triangle T(n, k)=(-1)^(n-k)*sum{j=0..n, binomial(n, k+j)}

T(n,k)=T(n-1,k-1)-3*T(n-1,k)+2*T(n-2,k-1)-2*T(n-2,k), T(0,0)=1, T(1,0)=-2, T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 12 2014