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A209749 Triangle of coefficients of polynomials u(n,x) jointly generated with A209750; see the Formula section.

%I A209749 #6 Mar 30 2012 18:58:15
%S A209749 1,1,2,2,4,3,2,8,9,4,3,11,21,17,5,3,17,37,47,29,6,4,21,63,101,95,46,7,
%T A209749 4,29,93,193,241,178,69,8,5,34,138,329,519,522,314,99,9,5,44,186,533,
%U A209749 999,1264,1050,527,137,10,6,50,255,805,1776,2710,2845,1991,848
%N A209749 Triangle of coefficients of polynomials u(n,x) jointly generated with A209750; see the Formula section.
%C A209749 Alternating row sums: 1,-1,1,-1,1,-1,1,-1,...
%C A209749 For a discussion and guide to related arrays, see A208510.
%F A209749 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209749 v(n,x)=u(n-1,x)+x*v(n-1,x)+1,
%F A209749 where u(1,x)=1, v(1,x)=1.
%e A209749 First five rows:
%e A209749 1
%e A209749 1...2
%e A209749 2...4....3
%e A209749 2...8....9....4
%e A209749 3...11...21...17...5
%e A209749 First three polynomials u(n,x): 1, 1 + 2x, 2 + 4x + 3x^2.
%t A209749 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209749 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209749 v[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1;
%t A209749 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209749 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209749 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209749 TableForm[cu]
%t A209749 Flatten[%]    (* A209749 *)
%t A209749 Table[Expand[v[n, x]], {n, 1, z}]
%t A209749 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209749 TableForm[cv]
%t A209749 Flatten[%]    (* A209750 *)
%Y A209749 Cf. A209750, A208510.
%K A209749 nonn,tabl
%O A209749 1,3
%A A209749 _Clark Kimberling_, Mar 14 2012