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A210194 Triangle of coefficients of polynomials v(n,x) jointly generated with A210193; see the Formula section.

%I A210194 #4 Mar 30 2012 18:58:16
%S A210194 1,2,3,3,11,3,4,26,20,3,5,50,74,29,3,6,85,204,149,38,3,7,133,469,547,
%T A210194 251,47,3,8,196,952,1618,1160,380,56,3,9,276,1764,4110,4234,2124,536,
%U A210194 65,3,10,375,3048,9318,13036,9262,3520,719,74,3,11,495,4983
%N A210194 Triangle of coefficients of polynomials v(n,x) jointly generated with A210193; see the Formula section.
%C A210194 For a discussion and guide to related arrays, see A208510.
%F A210194 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210194 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210194 where u(1,x)=1, v(1,x)=1.
%e A210194 First five rows:
%e A210194 1
%e A210194 2...3
%e A210194 3...11...3
%e A210194 4...26...20...3
%e A210194 5...50...74...29...3
%e A210194 First three polynomials v(n,x): 1, 2 + 3x , 3 + 11x + 3x^2.
%t A210194 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210194 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210194 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210194 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210194 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210194 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210194 TableForm[cu]
%t A210194 Flatten[%]   (* A210193 *)
%t A210194 Table[Expand[v[n, x]], {n, 1, z}]
%t A210194 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210194 TableForm[cv]
%t A210194 Flatten[%]  (* A210194 *)
%Y A210194 Cf. A210193, A208510.
%K A210194 nonn,tabl
%O A210194 1,2
%A A210194 _Clark Kimberling_, Mar 18 2012