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A209770 Triangle of coefficients of polynomials v(n,x) jointly generated with A209769; see the Formula section.

%I A209770 #5 Mar 30 2012 18:58:15
%S A209770 1,3,1,5,4,2,9,12,10,3,15,29,33,19,5,25,64,93,77,37,8,41,132,234,251,
%T A209770 171,69,13,67,261,548,719,629,362,127,21,109,500,1216,1884,2004,1482,
%U A209770 742,230,34,177,936,2592,4628,5784,5196,3342,1482,412,55,287
%N A209770 Triangle of coefficients of polynomials v(n,x) jointly generated with A209769; see the Formula section.
%C A209770 Column 1: A001595
%C A209770 Row n ends with F(n), where F=A000045, the Fibonacci numbers.
%C A209770 Row sums: 1,4,11,34,101,304,911,2734,... A060925
%C A209770 Alternating row sums: 1,2,3,4,5,6,7,.... A000027
%C A209770 For a discussion and guide to related arrays, see A208510.
%F A209770 u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
%F A209770 v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1,
%F A209770 where u(1,x)=1, v(1,x)=1.
%e A209770 First five rows:
%e A209770 1
%e A209770 3....1
%e A209770 5....4....2
%e A209770 9....12...10...3
%e A209770 15...29...33...19...5
%e A209770 First three polynomials v(n,x): 1, 3 + x , 5 + 4x + 2x^2.
%t A209770 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209770 u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209770 v[n_, x_] := (x + 1)*u[n - 1, x] + v[n - 1, x] + 1;
%t A209770 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209770 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209770 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209770 TableForm[cu]
%t A209770 Flatten[%]    (* A209769 *)
%t A209770 Table[Expand[v[n, x]], {n, 1, z}]
%t A209770 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209770 TableForm[cv]
%t A209770 Flatten[%]    (* A209770 *)
%Y A209770 Cf. A209669, A208510.
%K A209770 nonn,tabl
%O A209770 1,2
%A A209770 _Clark Kimberling_, Mar 15 2012