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A208931 Triangle of coefficients of polynomials u(n,x) jointly generated with A208932; see the Formula section.

%I A208931 #5 Mar 30 2012 18:58:14
%S A208931 1,1,2,1,8,4,1,18,20,8,1,32,64,56,16,1,50,160,224,136,32,1,72,340,680,
%T A208931 664,328,64,1,98,644,1736,2416,1872,760,128,1,128,1120,3920,7264,7856,
%U A208931 4984,1736,256,1,162,1824,8064,19056,26992,23768,12832,3896
%N A208931 Triangle of coefficients of polynomials u(n,x) jointly generated with A208932; see the Formula section.
%C A208931 For a discussion and guide to related arrays, see A208510.
%F A208931 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208931 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A208931 where u(1,x)=1, v(1,x)=1.
%e A208931 First five rows:
%e A208931 1
%e A208931 1...2
%e A208931 1...8....4
%e A208931 1...18...20...8
%e A208931 1...32...64...56...16
%e A208931 First five polynomials u(n,x):
%e A208931 1
%e A208931 1 + 2x
%e A208931 1 + 8x + 4x^2
%e A208931 1 + 18x + 20x^2 + 8x^3
%e A208931 1 + 32x + 64x^2 + 56x^3 + 16x^4
%t A208931 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208931 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208931 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A208931 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208931 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208931 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208931 TableForm[cu]
%t A208931 Flatten[%]    (* A208931 *)
%t A208931 Table[Expand[v[n, x]], {n, 1, z}]
%t A208931 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208931 TableForm[cv]
%t A208931 Flatten[%]    (* A208932 *)
%Y A208931 Cf. A208931, A208510.
%K A208931 nonn,tabl
%O A208931 1,3
%A A208931 _Clark Kimberling_, Mar 04 2012