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A181690 Riordan array T((1-x)^(-2) | 2x-1) read by rows.

%I A181690 #22 Sep 24 2018 22:06:05
%S A181690 -1,-4,1,-11,6,-1,-26,23,-8,1,-57,72,-39,10,-1,-120,201,-150,59,-12,1,
%T A181690 -247,522,-501,268,-83,14,-1,-502,1291,-1524,1037,-434,111,-16,1,
%U A181690 -1013,3084,-4339,3598,-1905,656,-143,18,-1,-2036,7181,-11762,11535,-7408,3217,-942,179,-20,1
%N A181690 Riordan array T((1-x)^(-2) | 2x-1) read by rows.
%C A181690 The first column is A000295 signed. - _Michel Marcus_, Feb 14 2014
%H A181690 Ana Luzón, <a href="http://arxiv.org/abs/0907.2328">Iterative Processes Related to Riordan Arrays: The Reciprocation and the Inversion of Power Series</a>, arXiv:0907.2328 [math.CO], 2009-2010; Discrete Math., 310 (2010), 3607-3618.
%H A181690 Ana Luzón and Manuel A. Morón, <a href="http://dx.doi.org/10.1016/j.laa.2008.12.001">Riordan matrices in the reciprocation of quadratic polynomials</a>, Linear Algebra Appl. 430 (2009), no. 8-9, 22542270.
%e A181690 Array begins:
%e A181690     -1;
%e A181690     -4,   1;
%e A181690    -11,   6,   -1;
%e A181690    -26,  23,   -8,  1;
%e A181690    -57,  72,  -39, 10,  -1;
%e A181690   -120, 201, -150, 59, -12, 1;
%e A181690   ...
%t A181690 t[n_, k_] := t[n, k] = If[n<0, 0, If[k==0, n+3-2^(n+2), If[k>n, 0, 2 t[n-1, k] - t[n-1, k-1]]]];
%t A181690 Table[t[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Sep 24 2018, from PARI *)
%o A181690 (PARI) t(n, k) = if (n < 0, 0, if (k == 0, n + 3 - 2^(n+2), if (k >n, 0, 2*tr(n-1, k) - tr(n-1, k-1)))); \\ _Michel Marcus_, Feb 14 2014
%Y A181690 Cf. A000295, A159856.
%K A181690 sign,tabl
%O A181690 0,2
%A A181690 _N. J. A. Sloane_, Nov 17 2010
%E A181690 a(0) corrected and more terms from _Michel Marcus_, Feb 14 2014