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A210750 Triangle of coefficients of polynomials v(n,x) jointly generated with A210749; see the Formula section.

%I A210750 #5 Mar 30 2012 18:58:17
%S A210750 1,2,3,4,8,7,7,21,24,15,12,46,78,64,31,20,96,205,247,160,63,33,190,
%T A210750 501,756,712,384,127,54,365,1140,2109,2483,1929,896,255,88,684,2480,
%U A210750 5404,7764,7538,5002,2048,511,143,1259,5199,13083,22070,26058
%N A210750 Triangle of coefficients of polynomials v(n,x) jointly generated with A210749; see the Formula section.
%C A210750 Row n starts with -1+F(n+2) and ends with -1+2^n, where F=A000045 (Fibonacci numbers).
%C A210750 For a discussion and guide to related arrays, see A208510.
%F A210750 u(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A210750 v(n,x)=(x+1)*u(n-1,x)+2x*v(n-1,x)+1,
%F A210750 where u(1,x)=1, v(1,x)=1.
%e A210750 First five rows:
%e A210750 1
%e A210750 2....3
%e A210750 4....8....7
%e A210750 7....21...24...15
%e A210750 12...46...78...64...31
%e A210750 First three polynomials v(n,x): 1, 2 + 3x, 4 + 8x +7x^2
%t A210750 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A210750 u[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A210750 v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A210750 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A210750 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A210750 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A210750 TableForm[cu]
%t A210750 Flatten[%]    (* A210749 *)
%t A210750 Table[Expand[v[n, x]], {n, 1, z}]
%t A210750 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A210750 TableForm[cv]
%t A210750 Flatten[%]    (* A210750 *)
%Y A210750 Cf. A210749, A208510.
%K A210750 nonn,tabl
%O A210750 1,2
%A A210750 _Clark Kimberling_, Mar 25 2012