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A237498 Riordan array (1/(1-x-x^2), x/(1+2*x)).

%I A237498 #17 Mar 15 2017 04:00:20
%S A237498 1,1,1,2,-1,1,3,4,-3,1,5,-5,10,-5,1,8,15,-25,20,-7,1,13,-22,65,-65,34,
%T A237498 -9,1,21,57,-152,195,-133,52,-11,1,34,-93,361,-542,461,-237,74,-13,1,
%U A237498 55,220,-815,1445,-1464,935,-385,100,-15,1,89,-385,1850,-3705
%N A237498 Riordan array (1/(1-x-x^2), x/(1+2*x)).
%C A237498 First column: Fibonacci numbers A000045(n+1).
%H A237498 Indranil Ghosh, <a href="/A237498/b237498.txt">Rows 0..100, flattened</a>
%F A237498 Sum_{k=0..n} T(n,k)*x^k = A000045(n+1), A098600(n), A000032(n+1), A027961(n+1), A027974(n) for x = 0, 1, 2, 3, 4 respectively.
%F A237498 T(n,k) = T(n-1,k-1) - T(n-1,k) + 3*T(n-2,k) - T(n-2,k-1) + 2*T(n-3,k) - T(n-3,k-1), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = -1, T(n,k) = 0 if k<0 or if k>n.
%F A237498 T(n,0) = T(n-1,0) + T(n-2,0) with T(0,0) = T(1,0) = 1, T(n,k) = T(n-1,k-1) - 2*T(n-1,k) for k>=1.
%F A237498 G.f.: (1+2*x)/((1+2*x-y*x)*(1-x-x^2)).
%e A237498 Triangle begins:
%e A237498    1;
%e A237498    1,    1;
%e A237498    2,   -1,    1;
%e A237498    3,    4,   -3,    1;
%e A237498    5,   -5,   10,   -5,   1;
%e A237498    8,   15,  -25,   20,  -7,   1;
%e A237498   13,  -22,   65,  -65,  34,  -9,  1;
%e A237498   ...
%e A237498 Production matrix is:
%e A237498    1,  1;
%e A237498    1, -2,  1;
%e A237498    2,  0, -2,  1;
%e A237498    4,  0,  0, -2,  1;
%e A237498    8,  0,  0,  0, -2,  1;
%e A237498   16,  0,  0,  0,  0, -2,  1;
%e A237498   32,  0,  0,  0,  0,  0, -2,  1;
%e A237498   64,  0,  0,  0,  0,  0,  0, -2,  1;
%e A237498   ...
%t A237498 nmax=10;Flatten[CoefficientList[Series[CoefficientList[Series[(1 + 2*x) / ((1 + 2*x - y*x) * (1 - x - x^2)), {x, 0, nmax }], x], {y, 0, nmax}], y]] (* _Indranil Ghosh_, Mar 15 2017 *)
%Y A237498 Columns: A000045, A084179.
%K A237498 easy,sign,tabl
%O A237498 0,4
%A A237498 _Philippe Deléham_, Feb 08 2014