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A210038 Triangle of coefficients of polynomials v(n,x) jointly generated with A210037; see the Formula section.

%I A210038 #4 Mar 30 2012 18:58:16
%S A210038 1,3,1,7,4,1,15,12,5,1,31,32,18,6,1,63,80,56,25,7,1,127,192,160,88,33,
%T A210038 8,1,255,448,432,280,129,42,9,1,511,1024,1120,832,450,180,52,10,1,
%U A210038 1023,2304,2816,2352,1452,681,242,63,11,1,2047,5120,6912,6400
%N A210038 Triangle of coefficients of polynomials v(n,x) jointly generated with A210037; see the Formula section.
%C A210038 For a discussion and guide to related arrays, see A208510.
%F A210038 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210038 v(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F A210038 where u(1,x)=1, v(1,x)=1.
%e A210038 First five rows:
%e A210038 1
%e A210038 3....1
%e A210038 7....4....1
%e A210038 15...12...5....1
%e A210038 31...32...18...6...1
%e A210038 First three polynomials v(n,x): 1, 3 + x , 7 + 4x + x^2.
%t A210038 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210038 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210038 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210038 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210038 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210038 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210038 TableForm[cu]
%t A210038 Flatten[%]    (* A210037 *)
%t A210038 Table[Expand[v[n, x]], {n, 1, z}]
%t A210038 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210038 TableForm[cv]
%t A210038 Flatten[%]    (* A210038 *)
%Y A210038 Cf. A210037, A208510.
%K A210038 nonn,tabl
%O A210038 1,2
%A A210038 _Clark Kimberling_, Mar 17 2012