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%I #5 Mar 30 2012 18:58:13
%S 1,1,1,1,3,3,1,5,9,7,1,7,17,25,17,1,9,27,55,69,41,1,11,39,99,171,187,
%T 99,1,13,53,159,341,515,501,239,1,15,69,237,599,1125,1515,1329,577,1,
%U 17,87,335,967,2141,3591,4373,3497,1393,1,19,107,455,1469,3713
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208611; see the Formula section.
%F u(n,x)=u(n-1,x)+x*v(n-1,x),
%F v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...1
%e 1...3...3
%e 1...5...9...7
%e 1...7...17...25...17
%e First five polynomials u(n,x):
%e 1
%e 1 + x
%e 1 + 3x + 3x^2
%e 1 + 5x + 9x^2 + 7x^3
%e 1 + 7x + 17x^2 + 25x^3 + 17x^4
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A208610 *)
%t Table[Expand[v[n, x]], {n, 1, z}]
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A208611 *)
%Y Cf. A208611.
%K nonn,tabl
%O 1,5
%A _Clark Kimberling_, Mar 01 2012
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