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A210199 Triangle of coefficients of polynomials u(n,x) jointly generated with A210200; see the Formula section.

%I A210199 #4 Mar 30 2012 18:58:16
%S A210199 1,3,6,2,11,7,2,19,19,9,2,32,44,30,11,2,53,94,83,43,13,2,87,190,207,
%T A210199 137,58,15,2,142,370,480,387,208,75,17,2,231,701,1057,1004,653,298,94,
%U A210199 19,2,375,1301,2238,2448,1865,1026,409,115,21,2,608,2376,4596
%N A210199 Triangle of coefficients of polynomials u(n,x) jointly generated with A210200; see the Formula section.
%C A210199 For a discussion and guide to related arrays, see A208510.
%F A210199 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210199 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A210199 where u(1,x)=1, v(1,x)=1.
%e A210199 First five rows:
%e A210199 1
%e A210199 3
%e A210199 6....2
%e A210199 11...7....2
%e A210199 19...19...9...2
%e A210199 First three polynomials u(n,x): 1, 3, 6 + 2x.
%t A210199 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210199 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210199 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210199 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210199 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210199 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210199 TableForm[cu]
%t A210199 Flatten[%]   (* A210199 *)
%t A210199 Table[Expand[v[n, x]], {n, 1, z}]
%t A210199 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210199 TableForm[cv]
%t A210199 Flatten[%]  (* A210200 *)
%Y A210199 Cf. A210200, A208510.
%K A210199 nonn,tabf
%O A210199 1,2
%A A210199 _Clark Kimberling_, Mar 18 2012