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A207627 Triangle of coefficients of polynomials u(n,x) jointly generated with A207628; see the Formula section.

%I A207627 #10 Sep 08 2013 19:59:30
%S A207627 1,2,3,4,4,10,8,5,18,28,16,6,28,64,72,32,7,40,120,200,176,64,8,54,200,
%T A207627 440,576,416,128,9,70,308,840,1456,1568,960,256,10,88,448,1456,3136,
%U A207627 4480,4096,2176,512,11,108,624,2352,6048,10752,13056,10368,4864
%N A207627 Triangle of coefficients of polynomials u(n,x) jointly generated with A207628; see the Formula section.
%C A207627 Column n is divisible by 2^(n-1); row n ends with 2^(n-1).
%F A207627 u(n,x)=u(n-1,x)+v(n-1,x),
%F A207627 v(n,x)=2x*u(n-1,x)+2x*v(n-1,x)+1,
%F A207627 where u(1,x)=1, v(1,x)=1.
%F A207627 The row sums =:  2, 7, 22, 67, ... are given by (5*3^n -1)/2 for n = 0, 1, 2, 3, ... . - _Philippe Deléham_, Feb 25 2012
%e A207627 First five rows:
%e A207627 1
%e A207627 2
%e A207627 3...4
%e A207627 4...10...8
%e A207627 5...18...28...16
%t A207627 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207627 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207627 v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
%t A207627 Table[Factor[u[n, x]], {n, 1, z}]
%t A207627 Table[Factor[v[n, x]], {n, 1, z}]
%t A207627 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207627 TableForm[cu]
%t A207627 Flatten[%]    (* A207625 *)
%t A207627 Table[Expand[v[n, x]], {n, 1, z}]
%t A207627 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207627 TableForm[cv]
%t A207627 Flatten[%]    (* A207626 *)
%Y A207627 Cf. A207628.
%K A207627 nonn,tabf
%O A207627 1,2
%A A207627 _Clark Kimberling_, Feb 21 2012