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

%I A210200 #5 Mar 30 2012 18:58:16
%S A210200 1,2,2,4,5,2,7,12,7,2,12,25,21,9,2,20,50,53,32,11,2,33,96,124,94,45,
%T A210200 13,2,54,180,273,250,150,60,15,2,88,331,577,617,445,223,77,17,2,143,
%U A210200 600,1181,1444,1212,728,315,96,19,2,232,1075,2358,3242,3101,2163
%N A210200 Triangle of coefficients of polynomials v(n,x) jointly generated with A210199; see the Formula section.
%C A210200 Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...
%C A210200 For a discussion and guide to related arrays, see A208510.
%F A210200 u(n,x)=u(n-1,x)+v(n-1,x)+1,
%F A210200 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A210200 where u(1,x)=1, v(1,x)=1.
%e A210200 First five rows:
%e A210200 1
%e A210200 2....2
%e A210200 4....5....2
%e A210200 7....12...7....2
%e A210200 12...25...21...9...2
%e A210200 First three polynomials v(n,x): 1, 2 + 2x , 4 + 5x + 2x^2.
%t A210200 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210200 u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
%t A210200 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210200 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210200 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210200 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210200 TableForm[cu]
%t A210200 Flatten[%]   (* A210199 *)
%t A210200 Table[Expand[v[n, x]], {n, 1, z}]
%t A210200 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210200 TableForm[cv]
%t A210200 Flatten[%]   (* A210200 *)
%Y A210200 Cf. A210199, A208510.
%K A210200 nonn,tabl
%O A210200 1,2
%A A210200 _Clark Kimberling_, Mar 18 2012