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A209170 Triangle of coefficients of polynomials u(n,x) jointly generated with A209171; see the Formula section.

%I A209170 #8 Apr 02 2012 03:38:36
%S A209170 1,2,1,5,6,2,11,20,13,3,23,57,57,27,5,47,149,202,144,53,8,95,369,633,
%T A209170 604,334,101,13,191,881,1831,2192,1618,733,188,21,383,2049,5007,7217,
%U A209170 6665,4022,1544,344,34,767,4673,13135,22153,24570,18519,9461
%N A209170 Triangle of coefficients of polynomials u(n,x) jointly generated with A209171; see the Formula section.
%C A209170 Row n ends with A000045 (Fibonacci numbers).
%C A209170 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209170 For a discussion and guide to related arrays, see A208510.
%F A209170 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209170 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A209170 where u(1,x)=1, v(1,x)=1.
%e A209170 First five rows:
%e A209170 1
%e A209170 2....1
%e A209170 5....6....2
%e A209170 11...20...13...3
%e A209170 23...57...57...27...5
%e A209170 First three polynomials v(n,x): 1, 2 + x, 5 + 6x + 2x^2.
%t A209170 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209170 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209170 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209170 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209170 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209170 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209170 TableForm[cu]
%t A209170 Flatten[%]    (* A209170 *)
%t A209170 Table[Expand[v[n, x]], {n, 1, z}]
%t A209170 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209170 TableForm[cv]
%t A209170 Flatten[%]    (* A209171 *)
%Y A209170 Cf. A209171, A208510.
%K A209170 nonn,tabl
%O A209170 1,2
%A A209170 _Clark Kimberling_, Mar 08 2012