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A210795 Triangle of coefficients of polynomials u(n,x) jointly generated with A210796; see the Formula section.

%I A210795 #5 Mar 30 2012 18:58:17
%S A210795 1,2,1,3,2,2,4,5,5,3,5,8,12,9,5,6,13,22,25,17,8,7,18,38,51,51,31,13,8,
%T A210795 25,59,98,115,101,56,21,9,32,88,166,238,248,196,100,34,10,41,124,270,
%U A210795 438,552,520,374,177,55,11,50,170,410,762,1090,1234,1064,704
%N A210795 Triangle of coefficients of polynomials u(n,x) jointly generated with A210796; see the Formula section.
%C A210795 Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).
%C A210795 Column 2: A000982
%C A210795 Column 3: A026035
%C A210795 For a discussion and guide to related arrays, see A208510.
%F A210795 u(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F A210795 v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x),
%F A210795 where u(1,x)=1, v(1,x)=1.
%e A210795 First five rows:
%e A210795 1
%e A210795 2...1
%e A210795 3...2...2
%e A210795 4...5...5....3
%e A210795 5...8...12...9...5
%e A210795 First three polynomials u(n,x): 1, 2 + x, 3 + 2x + 2x^2.
%t A210795 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210795 u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
%t A210795 d[x_] := h + x; e[x_] := p + x;
%t A210795 v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
%t A210795 j = 0; c = 1; h = 2; p = -1; f = 0;
%t A210795 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210795 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210795 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210795 TableForm[cu]
%t A210795 Flatten[%]   (* A210795 *)
%t A210795 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210795 TableForm[cv]
%t A210795 Flatten[%]   (* A210796 *)
%Y A210795 Cf. A210796, A208510.
%K A210795 nonn,tabl
%O A210795 1,2
%A A210795 _Clark Kimberling_, Mar 26 2012