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A210191 Triangle of coefficients of polynomials u(n,x) jointly generated with A210192; see the Formula section.

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