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A208915 Triangle of coefficients of polynomials u(n,x) jointly generated with A208916; see the Formula section.

%I A208915 #5 Mar 30 2012 18:58:14
%S A208915 1,1,2,1,4,6,1,6,12,14,1,8,18,36,38,1,10,24,66,108,94,1,12,30,104,210,
%T A208915 308,246,1,14,36,150,344,674,892,622,1,16,42,204,510,1224,2098,2500,
%U A208915 1606,1,18,48,266,708,1990,4024,6402,7052,4094,1,20,54,336,938
%N A208915 Triangle of coefficients of polynomials u(n,x) jointly generated with A208916; see the Formula section.
%C A208915 For a discussion and guide to related arrays, see A208510.
%F A208915 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208915 v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F A208915 where u(1,x)=1, v(1,x)=1.
%e A208915 First five rows:
%e A208915 1
%e A208915 1...2
%e A208915 1...4...6
%e A208915 1...6...12...14
%e A208915 1...8...18...36...38
%e A208915 First five polynomials u(n,x):
%e A208915 1
%e A208915 1 + 2x
%e A208915 1 + 4x + 6x^2
%e A208915 1 + 6x + 12x^2 + 14x^3
%e A208915 1 + 8x + 18x^2 + 36x^3 + 38x^4
%t A208915 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208915 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208915 v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A208915 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208915 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208915 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208915 TableForm[cu]
%t A208915 Flatten[%]    (* A208915 *)
%t A208915 Table[Expand[v[n, x]], {n, 1, z}]
%t A208915 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208915 TableForm[cv]
%t A208915 Flatten[%]    (* A208916 *)
%Y A208915 Cf. A208914, A208510.
%K A208915 nonn,tabl
%O A208915 1,3
%A A208915 _Clark Kimberling_, Mar 03 2012