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%I #14 Mar 31 2023 03:22:06
%S 1,3,1,6,4,1,12,11,5,1,24,28,17,6,1,48,68,51,24,7,1,96,160,142,82,32,
%T 8,1,192,368,376,255,122,41,9,1,384,832,960,744,417,172,51,10,1,768,
%U 1856,2384,2072,1323,639,233,62,11,1,1536,4096,5792,5568,3974
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A207614; see the Formula section.
%C Riordan array ((1 + z)/(1 - 2*z), z*(1 - z)/(1 - 2*z)). - _Peter Bala_, Dec 31 2015
%F u(n,x) = u(n-1,x) + v(n-1,x),
%F v(n,x) = u(n-1,x) + (x + 1)*v(n-1,x) + 1,
%F where u(1,x) = 1, v(1,x) = 1.
%e First five rows:
%e 1
%e 3 1
%e 6 4 1
%e 12 11 5 1
%e 24 28 17 6 1
%t u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1
%t Table[Factor[u[n, x]], {n, 1, z}]
%t Table[Factor[v[n, x]], {n, 1, z}]
%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t TableForm[cu]
%t Flatten[%] (* A207614 *)
%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[%] (* A207615 *)
%Y Cf. A207614, A208510, A003945, A011782.
%K nonn,tabl,easy
%O 1,2
%A _Clark Kimberling_, Feb 20 2012
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