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A208909 Triangle of coefficients of polynomials u(n,x) jointly generated with A208930; see the Formula section.

%I A208909 #5 Mar 30 2012 18:58:14
%S A208909 1,1,2,1,6,6,1,10,20,16,1,14,42,68,44,1,18,72,172,220,120,1,22,110,
%T A208909 344,648,696,328,1,26,156,600,1480,2336,2160,896,1,30,210,956,2900,
%U A208909 5984,8128,6608,2448,1,34,272,1428,5124,12984,23056,27536,19984
%N A208909 Triangle of coefficients of polynomials u(n,x) jointly generated with A208930; see the Formula section.
%C A208909 For a discussion and guide to related arrays, see A208510.
%F A208909 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208909 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A208909 where u(1,x)=1, v(1,x)=1.
%e A208909 First five rows:
%e A208909 1
%e A208909 1...2
%e A208909 1...6...6
%e A208909 1...10...20...16
%e A208909 1...14...42...68...44
%e A208909 First five polynomials u(n,x):
%e A208909 1
%e A208909 1 + 2x
%e A208909 1 + 6x + 6x^2
%e A208909 1 + 10x + 20x^2 + 16x^3
%e A208909 1 + 14x + 42x^2 + 68x^3 + 44x^4
%t A208909 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208909 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208909 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208909 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208909 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208909 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208909 TableForm[cu]
%t A208909 Flatten[%]    (* A208909 *)
%t A208909 Table[Expand[v[n, x]], {n, 1, z}]
%t A208909 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208909 TableForm[cv]
%t A208909 Flatten[%]    (* A208930 *)
%Y A208909 Cf. A208909, A208510.
%K A208909 nonn,tabl
%O A208909 1,3
%A A208909 _Clark Kimberling_, Mar 04 2012