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A208521 Triangle of coefficients of polynomials v(n,x) jointly generated with A208520; see the Formula section.

%I A208521 #5 Mar 30 2012 18:58:13
%S A208521 1,2,2,3,4,2,4,6,8,4,5,8,20,16,4,6,10,40,40,24,8,7,12,70,80,84,48,8,8,
%T A208521 14,112,140,224,168,64,16,9,16,168,224,504,448,288,128,16,10,18,240,
%U A208521 336,1008,1008,960,576,160,32,11,20,330,480,1848,2016,2640,1920
%N A208521 Triangle of coefficients of polynomials v(n,x) jointly generated with A208520; see the Formula section.
%F A208521 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208521 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A208521 where u(1,x)=1, v(1,x)=1.
%e A208521 First five rows:
%e A208521 1
%e A208521 2...2
%e A208521 3...4...2
%e A208521 4...6...8....4
%e A208521 5...8...20...16...4
%e A208521 First five polynomials v(n,x):
%e A208521 1
%e A208521 2 + 2x
%e A208521 3 + 4x + 2x^2
%e A208521 4 + 6x + 8x^2 + 4x^3
%e A208521 5 + 8x + 20x^2 + 16x^3 + 4x^4
%t A208521 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208521 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208521 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A208521 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208521 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208521 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208521 TableForm[cu]
%t A208521 Flatten[%]    (* A208520 *)
%t A208521 Table[Expand[v[n, x]], {n, 1, z}]
%t A208521 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208521 TableForm[cv]
%t A208521 Flatten[%]    (* A208521 *)
%Y A208521 Cf. A208520.
%K A208521 nonn,tabl
%O A208521 1,2
%A A208521 _Clark Kimberling_, Feb 28 2012