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

%I A209704 #6 Jul 12 2012 00:40:00
%S A209704 1,3,1,4,3,2,5,6,8,3,6,10,18,14,5,7,15,33,38,27,8,8,21,54,81,83,49,13,
%T A209704 9,28,82,150,197,170,89,21,10,36,118,253,401,448,342,159,34,11,45,163,
%U A209704 399,736,999,987,671,282,55,12,55,218,598,1253,1988,2387,2106
%N A209704 Triangle of coefficients of polynomials v(n,x) jointly generated with A209703; see the Formula section.
%C A209704 For n>1, row n starts with n+1, followed by the n-th
%C A209704 triangular number, and ends in F(n+1), where F=A000045
%C A209704 (Fibonacci numbers).
%C A209704 Column 3:  A166830.
%C A209704 Row sums:  A048654.
%C A209704 Alternating row sums: 1,2,3,4,5,6,7,8,9,...
%C A209704 For a discussion and guide to related arrays, see A208510.
%F A209704 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209704 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A209704 where u(1,x)=1, v(1,x)=1.
%e A209704 First five rows:
%e A209704 1
%e A209704 3...1
%e A209704 4...3....2
%e A209704 5...6....8....3
%e A209704 6...10...18...14...5
%e A209704 First three polynomials v(n,x): 1, 3 + x , 4 + 3x + 2x^2.
%t A209704 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209704 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209704 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A209704 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209704 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209704 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209704 TableForm[cu]
%t A209704 Flatten[%]  (* A209703 *)
%t A209704 Table[Expand[v[n, x]], {n, 1, z}]
%t A209704 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209704 TableForm[cv]
%t A209704 Flatten[%]  (* A209704 *)
%Y A209704 Cf. A209703, A208510.
%K A209704 nonn,tabl
%O A209704 1,2
%A A209704 _Clark Kimberling_, Mar 12 2012