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A209148 Triangle of coefficients of polynomials u(n,x) jointly generated with A209149; see the Formula section.

%I A209148 #14 Feb 14 2018 03:17:01
%S A209148 1,2,1,5,5,1,11,16,7,1,23,44,30,9,1,47,112,104,48,11,1,95,272,320,200,
%T A209148 70,13,1,191,640,912,720,340,96,15,1,383,1472,2464,2352,1400,532,126,
%U A209148 17,1,767,3328,6400,7168,5152,2464,784,160,19,1,1535,7424
%N A209148 Triangle of coefficients of polynomials u(n,x) jointly generated with A209149; see the Formula section.
%C A209148 Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,...
%C A209148 For a discussion and guide to related arrays, see A208510.
%F A209148 u(n,x) = u(n-1,x) + (x+1)*v(n-1,x),
%F A209148 v(n,x) = u(n-1,x) + (x+1)*v(n-1,x)+1,
%F A209148 where u(1,x) = 1, v(1,x) = 1.
%F A209148 T(n,k) = 3*T(n-1,k)+T(n-1,k-1)-2*T(n-2,k)-T(n-2,k-1), T(1,0)=T(2,1)=T(3,2)=1, T(2,0)=2, T(3,0)=T(3,1)=5, T(n,k)=0 if k<0 or if k>=n. - _Philippe Deléham_, Jan 17 2014
%e A209148 First five rows:
%e A209148   1
%e A209148   2....1
%e A209148   5....5....1
%e A209148   11...16...7....1
%e A209148   23...44...30...9...1
%e A209148 First three polynomials v(n,x): 1, 2 + x, 5 + 5x + x^2.
%t A209148 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A209148 u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t A209148 v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;
%t A209148 Table[Expand[u[n, x]], {n, 1, z/2}]
%t A209148 Table[Expand[v[n, x]], {n, 1, z/2}]
%t A209148 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A209148 TableForm[cu]
%t A209148 Flatten[%]    (* A209148 *)
%t A209148 Table[Expand[v[n, x]], {n, 1, z}]
%t A209148 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A209148 TableForm[cv]
%t A209148 Flatten[%]    (* A209149 *)
%Y A209148 Cf. A209149, A208510.
%K A209148 nonn,tabl
%O A209148 1,2
%A A209148 _Clark Kimberling_, Mar 07 2012
%E A209148 Example corrected by _Philippe Deléham_, Jan 17 2014