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A208512 Triangle of coefficients of polynomials v(n,x) jointly generated with A208511; see the Formula section.

%I A208512 #5 Mar 30 2012 18:58:13
%S A208512 1,2,2,2,5,4,2,7,12,8,2,9,21,28,16,2,11,32,58,64,32,2,13,45,101,152,
%T A208512 144,64,2,15,60,159,296,384,320,128,2,17,77,234,513,824,944,704,256,2,
%U A208512 19,96,328,822,1554,2208,2272,1536,512,2,21,117,443,1244,2685
%N A208512 Triangle of coefficients of polynomials v(n,x) jointly generated with A208511; see the Formula section.
%C A208512 Alternating row sums are signed Fibonacci numbers (A000045).
%F A208512 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208512 v(n,x)=u(n-1,x)+2x*v(n-1,x)+1,
%F A208512 where u(1,x)=1, v(1,x)=1.
%e A208512 First five rows:
%e A208512 1
%e A208512 2...2
%e A208512 2...5...4
%e A208512 2...7...12...8
%e A208512 2...9...21...28...16
%e A208512 First five polynomials v(n,x):
%e A208512 1
%e A208512 2 + 2x
%e A208512 2 + 5x + 4x^2
%e A208512 2 + 7x + 12x^2 + 8x^3
%e A208512 2 + 9x + 21x^2 + 28x^3 + 16x^4
%t A208512 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208512 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208512 v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208512 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208512 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208512 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208512 TableForm[cu]
%t A208512 Flatten[%]  (* A208511 *)
%t A208512 Table[Expand[v[n, x]], {n, 1, z}]
%t A208512 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208512 TableForm[cv]
%t A208512 Flatten[%]    (* A208512 *)
%Y A208512 Cf. A208511.
%K A208512 nonn,tabl
%O A208512 1,2
%A A208512 _Clark Kimberling_, Feb 28 2012