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%I #13 Mar 06 2017 10:46:59
%S 1,2,2,2,5,4,2,6,12,8,2,6,17,28,16,2,6,18,46,64,32,2,6,18,53,120,144,
%T 64,2,6,18,54,152,304,320,128,2,6,18,54,161,424,752,704,256,2,6,18,54,
%U 162,474,1152,1824,1536,512,2,6,18,54,162,485,1372,3056,4352
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A210561; see the Formula section.
%C Last term in row n: 2^(n-1)
%C Limiting row: 2*3^(n-1)
%C Alternating row sums: 1,0,1,0,1,0,1,0,...
%C For a discussion and guide to related arrays, see A208510.
%C u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
%C v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
%C where u(1,x)=1, v(1,x)=1.
%C First five rows:
%C 1
%C 2...2
%C 2...5...4
%C 2...6...12...8
%C 2...6...17...28...16
%C First three polynomials v(n,x): 1, 2 + 2x , 2 + 5x + 4x^2.
%C u[1, x_] := 1; v[1, x_] := 1; z = 16;
%C u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
%C v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
%C Table[Expand[u[n, x]], {n, 1, z/2}]
%C Table[Expand[v[n, x]], {n, 1, z/2}]
%C cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%C TableForm[cu]
%C Flatten[%] (* A210561 *)
%C Table[Expand[v[n, x]], {n, 1, z}]
%C cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%C TableForm[cv]
%C Flatten[%] (* A210562 *)
%C Cf. A210561, A208510.
%H P. Bala, <a href="/A081577/a081577.pdf">A note on the diagonals of a proper Riordan Array</a>
%F From _Peter Bala_, Mar 06 2017: (Start)
%F T(n,k) = 2*T(n-1,k-1) + T(n-2,k-1).
%F E.g.f for the n-th subdiagonal: exp(2*x)*(2 + 2*x + 2*x^2/2! + 2*x^3/3! + ... + 2*x^(n-1)/(n-1)! + x^n/n!).
%F Riordan array ((1 + x)/(1 - x), x*(2 + x)).
%F Row sums A005409 (except for the initial term).
%F (End)
%Y Row sums A005409. Cf. A208510, A210561.
%K nonn,tabl,easy
%O 1,2
%A _Clark Kimberling_, Mar 22 2012
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