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A208754 Triangle of coefficients of polynomials v(n,x) jointly generated with A208753; see the Formula section.

%I A208754 #6 Mar 30 2012 18:58:14
%S A208754 1,3,5,2,7,10,9,28,4,11,60,28,13,110,108,8,15,182,308,72,17,280,728,
%T A208754 352,16,19,408,1512,1248,176,21,570,2856,3600,1040,32,23,770,5016,
%U A208754 8976,4400,416,25,1012,8316,20064,14960,2880,64,27,1300,13156,41184
%N A208754 Triangle of coefficients of polynomials v(n,x) jointly generated with A208753; see the Formula section.
%C A208754 For a discussion and guide to related arrays, see A208510.
%F A208754 u(n,x)=u(n-1,x)+2x*v(n-1,x),
%F A208754 v(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A208754 where u(1,x)=1, v(1,x)=1.
%e A208754 First five rows:
%e A208754 1
%e A208754 3
%e A208754 5...2
%e A208754 7...10
%e A208754 9...28...4
%e A208754 First five polynomials v(n,x):
%e A208754 1
%e A208754 3
%e A208754 5 + 2x
%e A208754 7 + 10x
%e A208754 9 + 28x + 4x^2
%t A208754 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208754 u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
%t A208754 v[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A208754 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208754 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208754 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208754 TableForm[cu]
%t A208754 Flatten[%]    (* A208753 *)
%t A208754 Table[Expand[v[n, x]], {n, 1, z}]
%t A208754 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208754 TableForm[cv]
%t A208754 Flatten[%]    (* A208754 *)
%Y A208754 Cf. A208753, A208510.
%K A208754 nonn,tabf
%O A208754 1,2
%A A208754 _Clark Kimberling_, Mar 03 2012