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%I #5 Mar 30 2012 18:58:16
%S 1,3,5,3,7,10,3,9,21,16,3,11,36,47,22,3,13,55,104,85,28,3,15,78,195,
%T 236,135,34,3,17,105,328,535,456,197,40,3,19,136,511,1058,1227,788,
%U 271,46,3,21,171,752,1897,2820,2471,1256,357,52,3,23,210,1059,3160
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210192; see the Formula section.
%C Period of alternating row sums: (1,3,2,0)
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 3
%e 5...3
%e 7...10...3
%e 9...21...16...3
%e First three polynomials u(n,x): 1, 3, 5 + 3x.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A210191 *)
%t Table[Expand[v[n, x]], {n, 1, z}]
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A210192 *)
%Y Cf. A210192, A208510.
%K nonn,tabf
%O 1,2
%A _Clark Kimberling_, Mar 18 2012
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