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

%I A210037 #4 Mar 30 2012 18:58:16
%S A210037 1,3,7,1,15,5,1,31,17,6,1,63,49,24,7,1,127,129,80,32,8,1,255,321,240,
%T A210037 120,41,9,1,511,769,672,400,170,51,10,1,1023,1793,1792,1232,620,231,
%U A210037 62,11,1,2047,4097,4608,3584,2072,912,304,74,12,1,4095,9217
%N A210037 Triangle of coefficients of polynomials u(n,x) jointly generated with A210038; see the Formula section.
%C A210037 For a discussion and guide to related arrays, see A208510.
%F A210037 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210037 v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210037 where u(1,x)=1, v(1,x)=1.
%e A210037 First five rows:
%e A210037 1
%e A210037 3
%e A210037 7....1
%e A210037 15...5....1
%e A210037 31...17...6...1
%e A210037 First three polynomials u(n,x): 1, 3, 7 + x.
%t A210037 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210037 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210037 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210037 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210037 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210037 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210037 TableForm[cu]
%t A210037 Flatten[%]    (* A210037 *)
%t A210037 Table[Expand[v[n, x]], {n, 1, z}]
%t A210037 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210037 TableForm[cv]
%t A210037 Flatten[%]    (* A210038 *)
%Y A210037 Cf. A210038, A208510.
%K A210037 nonn,tabf
%O A210037 1,2
%A A210037 _Clark Kimberling_, Mar 17 2012