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A209703 Triangle of coefficients of polynomials u(n,x) jointly generated with A209704; see the Formula section.

%I A209703 #5 Mar 30 2012 18:58:15
%S A209703 1,0,2,0,3,3,0,4,6,5,0,5,10,14,8,0,6,15,28,28,13,0,7,21,48,66,55,21,0,
%T A209703 8,28,75,129,149,104,34,0,9,36,110,225,326,319,193,55,0,10,45,154,363,
%U A209703 626,774,661,352,89,0,11,55,208,553,1099,1625,1761,1332,634
%N A209703 Triangle of coefficients of polynomials u(n,x) jointly generated with A209704; see the Formula section.
%C A209703 For n>1, row n begins with 0, has second term n, and ends with F(n+1), where F=A000045 (Fibonacci numbers); for n>2, column 2 consists of triangular numbers.
%C A209703 Row sums:  A098790.
%C A209703 Alternating row sums: 1,-2,0,-3,-1,-4,-3,-5,-3,-6,,...
%C A209703 For a discussion and guide to related arrays, see A208510.
%F A209703 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209703 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A209703 where u(1,x)=1, v(1,x)=1.
%e A209703 First five rows:
%e A209703 1
%e A209703 0...2
%e A209703 0...3....3
%e A209703 0...4....6...5
%e A209703 0...5...10...14...8
%e A209703 First three polynomials v(n,x): 1, 2x, 3x + 3x^2.
%t A209703 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209703 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209703 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A209703 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209703 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209703 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209703 TableForm[cu]
%t A209703 Flatten[%]  (* A209703 *)
%t A209703 Table[Expand[v[n, x]], {n, 1, z}]
%t A209703 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209703 TableForm[cv]
%t A209703 Flatten[%]  (* A209704 *)
%Y A209703 Cf. A209704, A208510.
%K A209703 nonn,tabl
%O A209703 1,3
%A A209703 _Clark Kimberling_, Mar 12 2012