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A209694 Triangle of coefficients of polynomials v(n,x) jointly generated with A209693; see the Formula section.

%I A209694 #5 Mar 30 2012 18:58:15
%S A209694 1,3,1,4,6,1,5,13,10,1,6,22,32,15,1,7,33,71,66,21,1,8,46,131,186,121,
%T A209694 28,1,9,61,216,415,422,204,36,1,10,78,330,801,1121,862,323,45,1,11,97,
%U A209694 477,1400,2507,2689,1625,487,55,1,12,118,661,2276,4977,6902
%N A209694 Triangle of coefficients of polynomials v(n,x) jointly generated with A209693; see the Formula section.
%C A209694 Alternating row sums are periodic.  For a discussion and guide to related arrays, see A208510.
%F A209694 u(n,x)=x*u(n-1,x)+x*v(n-1,x),
%F A209694 v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209694 where u(1,x)=1, v(1,x)=1.
%e A209694 First five rows:
%e A209694 1
%e A209694 3...1
%e A209694 4...6....1
%e A209694 5...13...10...1
%e A209694 6...22...32...15...1
%e A209694 First three polynomials v(n,x): 1, 3 + x , 4 + 6x + x^2.
%t A209694 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209694 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
%t A209694 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209694 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209694 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209694 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209694 TableForm[cu]
%t A209694 Flatten[%]   (* A209693 *)
%t A209694 Table[Expand[v[n, x]], {n, 1, z}]
%t A209694 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209694 TableForm[cv]
%t A209694 Flatten[%]   (* A209694 *)
%Y A209694 Cf. A209693, A208510.
%K A209694 nonn,tabl
%O A209694 1,2
%A A209694 _Clark Kimberling_, Mar 12 2012