cp's OEIS Frontend

A208526 Triangle of coefficients of polynomials u(n,x) jointly generated with A208527; see the Formula section.

%I A208526 #5 Mar 30 2012 18:58:13
%S A208526 1,1,1,1,2,4,1,3,8,10,1,4,12,22,28,1,5,16,36,68,76,1,6,20,52,120,200,
%T A208526 208,1,7,24,70,184,376,592,568,1,8,28,90,260,608,1184,1736,1552,1,9,
%U A208526 32,112,348,900,2016,3672,5072,4240,1,10,36,136,448,1256,3120
%N A208526 Triangle of coefficients of polynomials u(n,x) jointly generated with A208527; see the Formula section.
%F A208526 u(n,x)=u(n-1,x)+x*v(n-1,x),
%F A208526 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A208526 where u(1,x)=1, v(1,x)=1.
%e A208526 First five rows:
%e A208526 1
%e A208526 1...1
%e A208526 1...2...4
%e A208526 1...3...8....10
%e A208526 1...4...12...22...28
%e A208526 First five polynomials u(n,x):
%e A208526 1
%e A208526 1 + x
%e A208526 1 + 2x + 4x^2
%e A208526 1 + 3x + 8x^2 + 10x^3
%e A208526 1 + 4x + 12x^2 + 22x^3 + 28x^4
%t A208526 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A208526 u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
%t A208526 v[n_, x_] := 2 x*u[n - 1, x] + 2 x*v[n - 1, x] + 1;
%t A208526 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A208526 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A208526 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A208526 TableForm[cu]
%t A208526 Flatten[%]  (* A208526 *)
%t A208526 Table[Expand[v[n, x]], {n, 1, z}]
%t A208526 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A208526 TableForm[cv]
%t A208526 Flatten[%]  (* A208527 *)
%Y A208526 Cf. A208527.
%K A208526 nonn,tabl
%O A208526 1,5
%A A208526 _Clark Kimberling_, Feb 29 2012