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A207619 Triangle of coefficients of polynomials v(n,x) jointly generated with A207618; see the Formula section.

%I A207619 #9 Mar 31 2023 03:22:31
%S A207619 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 A207619 96,1,9,41,122,255,376,368,192,1,10,51,172,417,744,960,832,384,1,11,
%U A207619 62,233,639,1323,2072,2384,1856,768,1,12,74,306,933,2184,3974
%N A207619 Triangle of coefficients of polynomials v(n,x) jointly generated with A207618; see the Formula section.
%F A207619 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 A207619 First five rows:
%e A207619 1
%e A207619 1...3
%e A207619 1...4...6
%e A207619 1...5...11...12
%e A207619 1...6...17...28...24
%t A207619 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207619 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207619 v[n_, x_] := x*u[n - 1, x] + 2 x*v[n - 1, x] + 1
%t A207619 Table[Factor[u[n, x]], {n, 1, z}]
%t A207619 Table[Factor[v[n, x]], {n, 1, z}]
%t A207619 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207619 TableForm[cu]
%t A207619 Flatten[%]    (* A207618 *)
%t A207619 Table[Expand[v[n, x]], {n, 1, z}]
%t A207619 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207619 TableForm[cv]
%t A207619 Flatten[%]    (* A207619 *)
%Y A207619 Cf. A207618.
%K A207619 nonn,tabl
%O A207619 1,3
%A A207619 _Clark Kimberling_, Feb 20 2012