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%I #9 Mar 31 2023 03:22:31
%S 1,1,3,1,4,6,1,5,11,12,1,6,17,28,24,1,7,24,51,68,48,1,8,32,82,142,160,
%T 96,1,9,41,122,255,376,368,192,1,10,51,172,417,744,960,832,384,1,11,
%U 62,233,639,1323,2072,2384,1856,768,1,12,74,306,933,2184,3974
%N Triangle of coefficients of polynomials v(n,x) jointly generated with A207618; see the Formula section.
%F u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=xu(n-1,x)+2x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1.
%e First five rows:
%e 1
%e 1...3
%e 1...4...6
%e 1...5...11...12
%e 1...6...17...28...24
%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_] := x*u[n - 1, x] + 2 x*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[%] (* A207618 *)
%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[%] (* A207619 *)
%Y Cf. A207618.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Feb 20 2012
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