cp's OEIS Frontend

A209157 Triangle of coefficients of polynomials v(n,x) jointly generated with A209154; see the Formula section.

%I A209157 #7 Jul 12 2012 00:40:00
%S A209157 1,2,2,3,6,2,4,14,12,4,5,28,40,24,4,6,50,104,96,40,8,7,82,234,304,204,
%T A209157 72,8,8,126,476,820,768,408,112,16,9,184,896,1968,2408,1760,768,192,
%U A209157 16,10,258,1584,4320,6640,6288,3776,1408,288,32,11,350,2658
%N A209157 Triangle of coefficients of polynomials v(n,x) jointly generated with A209154; see the Formula section.
%C A209157 Last number of each row is a power of 2.
%C A209157 (n-th alternating row sum)=2-n for n>1.
%C A209157 For a discussion and guide to related arrays, see A208510.
%F A209157 u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F A209157 v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
%F A209157 where u(1,x)=1, v(1,x)=1.
%e A209157 First five rows:
%e A209157 1
%e A209157 2...2
%e A209157 3...6....2
%e A209157 4...14...12...4
%e A209157 5...28...40...24...4
%e A209157 First three polynomials v(n,x): 1, 2 + 2x, 3 + 6x + x^2.
%t A209157 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209157 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209157 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
%t A209157 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209157 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209157 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209157 TableForm[cu]
%t A209157 Flatten[%]    (* A209154 *)
%t A209157 Table[Expand[v[n, x]], {n, 1, z}]
%t A209157 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209157 TableForm[cv]
%t A209157 Flatten[%]    (* A209157 *)
%Y A209157 Cf. A209154, A208510.
%K A209157 nonn,tabl
%O A209157 1,2
%A A209157 _Clark Kimberling_, Mar 07 2012