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%I #5 Mar 30 2012 18:58:17
%S 1,1,1,1,3,2,1,4,5,3,1,6,10,10,5,1,7,16,22,18,8,1,9,24,42,47,33,13,1,
%T 10,33,69,98,95,59,21,1,12,44,108,182,220,188,105,34,1,13,56,156,308,
%U 444,472,363,185,55,1,15,70,220,490,818,1034,985,690,324,89,1
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210798; see the Formula section.
%C Row n starts with 1 and ends with F(n), where F=A000045 (Fibonacci numbers).
%C Column 2: A032766
%C Column 3: A001859
%C Row sums: A099232
%C Alternating row sums: A008346
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+x*v(n-1,x),
%F v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...1
%e 1...3...2
%e 1...4...5....3
%e 1...6...10...10...5
%e First three polynomials u(n,x): 1, 1 + x, 1 + 3x + 2x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
%t d[x_] := h + x; e[x_] := p + x;
%t v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
%t j = 0; c = 0; h = 2; p = -1; f = 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A210797 *)
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210798 *)
%t Table[u[n, x] /. x -> 1, {n, 1, z}] (* A099232 *)
%t Table[v[n, x] /. x -> 1, {n, 1, z}] (* A006130 *)
%t Table[u[n, x] /. x -> -1, {n, 1, z}] (* A008346 *)
%t Table[v[n, x] /. x -> -1, {n, 1, z}] (* A039834 *)
%Y Cf. A210798, A208510.
%K nonn,tabl
%O 1,5
%A _Clark Kimberling_, Mar 26 2012
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