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%I #5 Mar 30 2012 18:58:15
%S 1,2,1,4,4,1,7,10,5,1,11,21,17,7,1,16,40,46,28,8,1,22,71,107,87,39,10,
%T 1,29,119,224,232,144,55,11,1,37,190,434,555,443,226,70,13,1,46,291,
%U 792,1221,1198,773,328,91,14,1,56,430,1377,2511,2942,2318,1255
%N Triangle of coefficients of polynomials u(n,x) jointly generated with A208335; see the Formula section.
%C Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
%C For a discussion and guide to related arrays, see A208510.
%F u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
%F v(n,x)=x*u(n-1,x)+v(n-1,x)+1,
%F where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 2...1
%e 4...4.....1
%e 7...10....5....1
%e 11...21...17...7...1
%e First three polynomials v(n,x): 1, 2 + x, 4 + 4x + x^2.
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
%t v[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;
%t Table[Expand[u[n, x]], {n, 1, z/2}]
%t Table[Expand[v[n, x]], {n, 1, z/2}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A209150 *)
%t Table[Expand[v[n, x]], {n, 1, z}]
%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t TableForm[cv]
%t Flatten[%] (* A208335 *)
%Y Cf. A208335, A208510.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Mar 07 2012
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