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A209748 Triangle of coefficients of polynomials v(n,x) jointly generated with A209747; see the Formula section.

%I A209748 #5 Mar 30 2012 18:58:15
%S A209748 1,3,5,2,9,6,2,15,16,8,2,25,36,26,10,2,41,76,70,38,12,2,67,152,172,
%T A209748 118,52,14,2,109,294,394,328,182,68,16,2,177,554,860,840,562,264,86,
%U A209748 18,2,287,1024,1808,2028,1584,894,366,106,20,2,465,1864,3692,4676
%N A209748 Triangle of coefficients of polynomials v(n,x) jointly generated with A209747; see the Formula section.
%C A209748 Alternating row sums: 1,3,3,5,5,7,7,9,9,...
%C A209748 For a discussion and guide to related arrays, see A208510.
%F A209748 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209748 v(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A209748 where u(1,x)=1, v(1,x)=1.
%e A209748 First five rows:
%e A209748 1
%e A209748 3
%e A209748 5....2
%e A209748 9....6....2
%e A209748 15...16...8...2
%e A209748 First three polynomials v(n,x): 1, 3, 5 + 2x.
%t A209748 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209748 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209748 v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A209748 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209748 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209748 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209748 TableForm[cu]
%t A209748 Flatten[%]    (* A209747 *)
%t A209748 Table[Expand[v[n, x]], {n, 1, z}]
%t A209748 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209748 TableForm[cv]
%t A209748 Flatten[%]    (* A209748 *)
%Y A209748 Cf. A209647, A208510.
%K A209748 nonn,tabf
%O A209748 1,2
%A A209748 _Clark Kimberling_, Mar 13 2012