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A210201 Triangle of coefficients of polynomials u(n,x) jointly generated with A210202; see the Formula section.

%I A210201 #4 Mar 30 2012 18:58:16
%S A210201 1,3,6,3,11,10,6,19,27,23,12,32,62,73,52,24,53,132,193,187,116,48,87,
%T A210201 266,468,552,462,256,96,142,517,1061,1482,1495,1112,560,192,231,978,
%U A210201 2297,3688,4369,3896,2624,1216,384,375,1813,4797,8703,11758
%N A210201 Triangle of coefficients of polynomials u(n,x) jointly generated with A210202; see the Formula section.
%C A210201 Row sums:  3^(n-1)
%C A210201 For a discussion and guide to related arrays, see A208510.
%F A210201 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210201 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A210201 where u(1,x)=1, v(1,x)=1.
%e A210201 First five rows:
%e A210201 1
%e A210201 3
%e A210201 6....3
%e A210201 11...10...6
%e A210201 19...27...23...12
%e A210201 First three polynomials u(n,x): 1, 3, 6 + 3x.
%t A210201 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210201 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210201 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210201 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210201 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210201 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210201 TableForm[cu]
%t A210201 Flatten[%]   (* A210201 *)
%t A210201 Table[Expand[v[n, x]], {n, 1, z}]
%t A210201 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210201 TableForm[cv]
%t A210201 Flatten[%]   (* A210202 *)
%Y A210201 Cf. A210202, A208510.
%K A210201 nonn,tabf
%O A210201 1,2
%A A210201 _Clark Kimberling_, Mar 18 2012