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A208922 Triangle of coefficients of polynomials v(n,x) jointly generated with A208921; see the Formula section.

%I A208922 #6 Mar 30 2012 18:58:14
%S A208922 1,3,1,5,4,2,7,13,12,2,9,32,40,16,4,11,65,108,80,36,4,13,116,258,288,
%T A208922 180,48,8,15,189,560,842,700,324,96,8,17,288,1120,2144,2312,1536,640,
%U A208922 128,16,19,417,2088,4944,6728,5832,3232,1088,240,16,21,580,3666
%N A208922 Triangle of coefficients of polynomials v(n,x) jointly generated with A208921; see the Formula section.
%C A208922 Alternating row sums:  1,2,3,4,5,6,7,8,9,10,...
%C A208922 For a discussion and guide to related arrays, see A208510.
%F A208922 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208922 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A208922 where u(1,x)=1, v(1,x)=1.
%e A208922 First five rows:
%e A208922 1
%e A208922 3...1
%e A208922 5...4....2
%e A208922 7...13...12...2
%e A208922 9...32...40...16...4
%e A208922 First five polynomials v(n,x):
%e A208922 1
%e A208922 3 + x
%e A208922 5 + 4x + 2x^2
%e A208922 7 + 13x + 12x^2 + 2x^3
%e A208922 9 + 32x + 40x^2 + 16x^3 + 4x^4
%t A208922 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208922 u[n_, x_] := u[n - 1, x] + 2x*v[n - 1, x];
%t A208922 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A208922 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208922 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208922 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208922 TableForm[cu]
%t A208922 Flatten[%]    (* A208921 *)
%t A208922 Table[Expand[v[n, x]], {n, 1, z}]
%t A208922 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208922 TableForm[cv]
%t A208922 Flatten[%]    (* A208922 *)
%Y A208922 Cf. A208921, A208510.
%K A208922 nonn,tabl
%O A208922 1,2
%A A208922 _Clark Kimberling_, Mar 04 2012