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A210222 Triangle of coefficients of polynomials v(n,x) jointly generated with A104698; see the Formula section.

%I A210222 #7 Mar 30 2012 18:58:16
%S A210222 1,2,2,3,6,2,4,12,10,2,5,20,28,14,2,6,30,60,52,18,2,7,42,110,140,84,
%T A210222 22,2,8,56,182,310,276,124,26,2,9,72,280,602,726,484,172,30,2,10,90,
%U A210222 408,1064,1638,1486,780,228,34,2,11,110,570,1752,3304,3850,2750
%N A210222 Triangle of coefficients of polynomials v(n,x) jointly generated with A104698; see the Formula section.
%C A210222 Period of alternating row sums: (1,0,-1,0)
%C A210222 For a discussion and guide to related arrays, see A208510.
%F A210222 u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F A210222 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A210222 where u(1,x)=1, v(1,x)=1.
%e A210222 First five rows:
%e A210222 1
%e A210222 2...2
%e A210222 3...6....2
%e A210222 4...12...10...2
%e A210222 5...20...28...14...2
%e A210222 First three polynomials v(n,x): 1, 2 + 2x , 3 + 6x + 2x^2.
%t A210222 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210222 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210222 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A210222 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210222 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210222 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210222 TableForm[cu]
%t A210222 Flatten[%]     (* A104698 *)
%t A210222 Table[Expand[v[n, x]], {n, 1, z}]
%t A210222 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210222 TableForm[cv]
%t A210222 Flatten[%]     (* A210222 *)
%Y A210222 Cf. A104698, A208510.
%K A210222 nonn,tabl
%O A210222 1,2
%A A210222 _Clark Kimberling_, Mar 19 2012