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A208660 Triangle of coefficients of polynomials u(n,x) jointly generated with A208904; see the Formula section.

%I A208660 #8 Mar 30 2012 18:58:14
%S A208660 1,1,2,1,8,2,1,18,14,2,1,32,52,20,2,1,50,140,104,26,2,1,72,310,380,
%T A208660 174,32,2,1,98,602,1106,806,262,38,2,1,128,1064,2744,2924,1472,368,44,
%U A208660 2,1,162,1752,6048,8892,6412,2432,492,50,2,1,200,2730,12168,23652
%N A208660 Triangle of coefficients of polynomials u(n,x) jointly generated with A208904; see the Formula section.
%C A208660 For a discussion and guide to related arrays, see A208510.
%F A208660 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208660 v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A208660 where u(1,x)=1, v(1,x)=1.
%e A208660 First five rows:
%e A208660 1
%e A208660 1...2
%e A208660 1...8....2
%e A208660 1...18...14...2
%e A208660 1...32...52...20...2
%e A208660 First five polynomials u(n,x):
%e A208660 1
%e A208660 1 + 2x
%e A208660 1 + 8x + 2x^2
%e A208660 1 + 18x + 14x^2 + 2x^3
%e A208660 1 + 32x + 52x^2 + 20x^3 + 2x^4
%t A208660 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208660 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208660 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A208660 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208660 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208660 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208660 TableForm[cu]
%t A208660 Flatten[%]    (* A208660 *)
%t A208660 Table[Expand[v[n, x]], {n, 1, z}]
%t A208660 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208660 TableForm[cv]
%t A208660 Flatten[%]    (* A208904 *)
%Y A208660 Cf. A208904, A208510.
%K A208660 nonn,tabl
%O A208660 1,3
%A A208660 _Clark Kimberling_, Mar 03 2012