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A210555 Triangle of coefficients of polynomials u(n,x) jointly generated with A210556; see the Formula section.

%I A210555 #5 Mar 30 2012 18:58:16
%S A210555 1,1,2,1,3,4,1,4,7,8,1,5,10,17,16,1,6,13,28,39,32,1,7,16,41,70,89,64,
%T A210555 1,8,19,56,109,176,199,128,1,9,22,73,156,297,426,441,256,1,10,25,92,
%U A210555 211,456,765,1020,967,512,1,11,28,113,274,657,1236,1953,2398
%N A210555 Triangle of coefficients of polynomials u(n,x) jointly generated with A210556; see the Formula section.
%C A210555 For a discussion and guide to related arrays, see A208510.
%F A210555 u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%F A210555 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A210555 where u(1,x)=1, v(1,x)=1.
%e A210555 First five rows:
%e A210555 1
%e A210555 1...2
%e A210555 1...3...4
%e A210555 1...4...7....8
%e A210555 1...5...10...17...16
%e A210555 First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 4x^2.
%t A210555 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210555 u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A210555 v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210555 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210555 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210555 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210555 TableForm[cu]
%t A210555 Flatten[%]   (* A208341 *)
%t A210555 Table[Expand[v[n, x]], {n, 1, z}]
%t A210555 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210555 TableForm[cv]
%t A210555 Flatten[%]   (* A210554 *)
%Y A210555 Cf. A210554, A208510.
%K A210555 nonn,tabl
%O A210555 1,3
%A A210555 _Clark Kimberling_, Mar 22 2012