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A209758 Triangle of coefficients of polynomials v(n,x) jointly generated with A210041; see the Formula section.

%I A209758 #5 Mar 30 2012 18:58:15
%S A209758 1,1,3,1,5,6,1,7,13,12,1,9,22,32,24,1,11,33,63,76,48,1,13,46,107,170,
%T A209758 176,96,1,15,61,166,321,440,400,192,1,17,78,242,546,912,1104,896,384,
%U A209758 1,19,97,337,864,1683,2488,2704,1984,768,1,21,118,453,1296,2865
%N A209758 Triangle of coefficients of polynomials v(n,x) jointly generated with A210041; see the Formula section.
%C A209758 Row sums:  -1+(odd-indexed Fibonacci numbers)
%C A209758 For a discussion and guide to related arrays, see A208510.
%F A209758 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A209758 v(n,x)=x*u(n-1,x)+2x*v(n-1,x)+1,
%F A209758 where u(1,x)=1, v(1,x)=1.
%e A209758 First five rows:
%e A209758 1
%e A209758 1...3
%e A209758 1...5...6
%e A209758 1...7...13...12
%e A209758 1...9...22...32...24
%e A209758 First three polynomials v(n,x): 1, 1 + 3x , 1 + 5x + 6x^2.
%t A209758 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209758 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A209758 v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A209758 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209758 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209758 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209758 TableForm[cu]
%t A209758 Flatten[%]    (* A210041 *)
%t A209758 Table[Expand[v[n, x]], {n, 1, z}]
%t A209758 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209758 TableForm[cv]
%t A209758 Flatten[%]    (* A209758 *)
%Y A209758 Cf. A210041, A208510.
%K A209758 nonn,tabl
%O A209758 1,3
%A A209758 _Clark Kimberling_, Mar 17 2012