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A208908 Triangle of coefficients of polynomials v(n,x) jointly generated with A208923; see the Formula section.

%I A208908 #5 Mar 30 2012 18:58:14
%S A208908 1,2,2,2,5,4,2,9,15,8,2,13,33,37,16,2,17,59,103,91,32,2,21,93,221,297,
%T A208908 213,64,2,25,135,407,739,807,491,128,2,29,185,677,1553,2285,2105,1109,
%U A208908 256,2,33,243,1047,2907,5391,6675,5319,2475,512,2,37,309,1533
%N A208908 Triangle of coefficients of polynomials v(n,x) jointly generated with A208923; see the Formula section.
%C A208908 Alternating row sums: 1,0,1,0,1,0,1,0,1,0,1,0,...
%C A208908 For a discussion and guide to related arrays, see A208510.
%F A208908 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208908 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A208908 where u(1,x)=1, v(1,x)=1.
%e A208908 First five rows:
%e A208908 1
%e A208908 2...2
%e A208908 2...5....4
%e A208908 2...9...15...8
%e A208908 2...13...33...37...16
%e A208908 First five polynomials v(n,x):
%e A208908 1
%e A208908 2 + 2x
%e A208908 2 + 5x + 4x^2
%e A208908 2 + 9x + 15x^2 + 8x^3
%e A208908 2 + 13x + 33x^2 + 37x^3 + 16x^4
%t A208908 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208908 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208908 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A208908 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208908 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208908 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208908 TableForm[cu]
%t A208908 Flatten[%]    (* A208923 *)
%t A208908 Table[Expand[v[n, x]], {n, 1, z}]
%t A208908 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208908 TableForm[cv]
%t A208908 Flatten[%]    (* A208908 *)
%Y A208908 Cf. A208923, A208510.
%K A208908 nonn,tabl
%O A208908 1,2
%A A208908 _Clark Kimberling_, Mar 04 2012