A080246 - OEIS

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A080246

Signed version of A035607.

1, -2, 1, 2, -4, 1, -2, 8, -6, 1, 2, -12, 18, -8, 1, -2, 16, -38, 32, -10, 1, 2, -20, 66, -88, 50, -12, 1, -2, 24, -102, 192, -170, 72, -14, 1, 2, -28, 146, -360, 450, -292, 98, -16, 1, -2, 32, -198, 608, -1002, 912, -462, 128, -18, 1, 2, -36, 258, -952, 1970, -2364

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OFFSET

0,2

COMMENTS

Written as lower triangular matrix this has inverse A080247. Row sums are (1,-1,-1,1,1,-1,-1,1,1,...) Diagonal sums are signed tribonacci numbers A078042

Riordan array((1-x)/(1+x), x*(1-x)/(1+x)). - Philippe Deléham, Jan 05 2014

LINKS

Table of n, a(n) for n=0..60.

Paul Barry, Laurent Biorthogonal Polynomials and Riordan Arrays, arXiv preprint arXiv:1311.2292, 2013

Heinrich Niederhausen, Inverses of Motzkin and Schroeder Paths, arXiv preprint arXiv:1105.3713, 2011.

FORMULA

Columns are generated by (1-x)^k/(1+x)^k

T(n,k)=(-1)^(n+k)*A113413(n,k). - Philippe Deléham, Jan 05 2014

T(n,k)=T(n-1,k-1)-T(n-1,k)-T(n-2,k-1), 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 05 2014

EXAMPLE

Rows are {1}, {-2,1}, {2,-4,1}, {-2,8,-6,1}, ...

CROSSREFS