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A210755 Triangle of coefficients of polynomials u(n,x) jointly generated with A210756; see the Formula section.

%I A210755 #6 Mar 30 2012 18:58:17
%S A210755 1,2,3,3,11,7,4,26,38,17,5,50,124,121,41,6,85,314,499,362,99,7,133,
%T A210755 679,1555,1805,1043,239,8,196,1316,4054,6672,6096,2926,577,9,276,2352,
%U A210755 9318,20326,26048,19610,8049,1393,10,375,3948,19482,53932,90706
%N A210755 Triangle of coefficients of polynomials u(n,x) jointly generated with A210756; see the Formula section.
%C A210755 Row n starts with n and ends with A001333(n).
%C A210755 Column 2: A051925
%C A210755 Row sums: A002450
%C A210755 Alternating row sums: 1,-1,-1,-1,-1,-1,...
%C A210755 For a discussion and guide to related arrays, see A208510.
%F A210755 u(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A210755 v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,
%F A210755 where u(1,x)=1, v(1,x)=1.
%e A210755 First five rows:
%e A210755 1
%e A210755 2...3
%e A210755 3...11...7
%e A210755 4...26...38....17
%e A210755 5...50...124...121...41
%e A210755 First three polynomials u(n,x): 1, 2 + 3x, 3 + 11x + 7x^2.
%t A210755 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210755 u[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210755 v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A210755 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210755 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210755 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210755 TableForm[cu]
%t A210755 Flatten[%]    (* A210755 *)
%t A210755 Table[Expand[v[n, x]], {n, 1, z}]
%t A210755 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210755 TableForm[cv]
%t A210755 Flatten[%]    (* A210756 *)
%t A210755 Table[u[n, x] /. x -> 1, {n, 1, z}]  (* A002450 *)
%t A210755 Table[v[n, x] /. x -> 1, {n, 1, z}]  (* A002450 *)
%Y A210755 Cf. A210754, A208510.
%K A210755 nonn,tabl
%O A210755 1,2
%A A210755 _Clark Kimberling_, Mar 25 2012