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A210226 Triangle of coefficients of polynomials v(n,x) jointly generated with A210225; see the Formula section.

%I A210226 #5 Mar 30 2012 18:58:16
%S A210226 1,2,3,3,9,5,4,18,24,7,5,30,66,51,9,6,45,140,189,94,11,7,63,255,505,
%T A210226 457,157,13,8,84,420,1110,1516,976,244,15,9,108,644,2142,3986,3960,
%U A210226 1896,359,17,10,135,936,3766,8960,12338,9276,3419,506,19,11,165
%N A210226 Triangle of coefficients of polynomials v(n,x) jointly generated with A210225; see the Formula section.
%C A210226 For a discussion and guide to related arrays, see A208510.
%F A210226 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210226 v(n,x)=2x*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210226 where u(1,x)=1, v(1,x)=1.
%e A210226 First five rows:
%e A210226 1
%e A210226 2...3
%e A210226 3...9....5
%e A210226 4...18...24...7
%e A210226 5...30...66...51...9
%e A210226 First three polynomials v(n,x): 1, 2 + 3x , 3 + 9x + 5x^2.
%t A210226 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210226 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210226 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210226 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210226 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210226 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210226 TableForm[cu]
%t A210226 Flatten[%]     (* A210225 *)
%t A210226 Table[Expand[v[n, x]], {n, 1, z}]
%t A210226 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210226 TableForm[cv]
%t A210226 Flatten[%]     (* A210226 *)
%Y A210226 Cf. A210225, A208510.
%K A210226 nonn,tabl
%O A210226 1,2
%A A210226 _Clark Kimberling_, Mar 20 2012