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A209579 Triangle of coefficients of polynomials u(n,x) jointly generated with A209580; see the Formula section.

%I A209579 #5 Mar 30 2012 18:58:15
%S A209579 1,1,1,2,3,1,2,6,6,1,3,9,14,10,1,3,14,28,29,15,1,4,18,48,71,55,21,1,4,
%T A209579 25,75,139,158,97,28,1,5,30,112,251,356,321,161,36,1,5,39,156,413,724,
%U A209579 828,609,254,45,1,6,45,215,645,1321,1874,1782,1094,384,55,1,6
%N A209579 Triangle of coefficients of polynomials u(n,x) jointly generated with A209580; see the Formula section.
%C A209579 For a discussion and guide to related arrays, see A208510.
%F A209579 u(n,x)=x*u(n-1,x)+v(n-1,x),
%F A209579 v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%F A209579 where u(1,x)=1, v(1,x)=1.
%e A209579 First five rows:
%e A209579 1
%e A209579 1...1
%e A209579 2...3....1
%e A209579 2...6....6....1
%e A209579 3...9....14...10...1
%e A209579 First three polynomials v(n,x): 1, 1 + x, 2 + 3x + x^2.
%t A209579 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209579 u[n_, x_] := x*u[n - 1, x] + v[n - 1, x];
%t A209579 v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%t A209579 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209579 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209579 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209579 TableForm[cu]
%t A209579 Flatten[%]   (* A209579 *)
%t A209579 Table[Expand[v[n, x]], {n, 1, z}]
%t A209579 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209579 TableForm[cv]
%t A209579 Flatten[%]   (* A209580 *)
%Y A209579 Cf. A209580, A208510.
%K A209579 nonn,tabl
%O A209579 1,4
%A A209579 _Clark Kimberling_, Mar 11 2012