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A207623 Triangle of coefficients of polynomials v(n,x) jointly generated with A207622; see the Formula section.

%I A207623 #9 Mar 31 2023 03:22:59
%S A207623 1,2,2,3,6,4,14,4,5,28,20,6,50,64,8,7,82,164,56,8,126,364,232,16,9,
%T A207623 184,728,736,144,10,258,1344,1968,736,32,11,350,2328,4656,2800,352,12,
%U A207623 462,3828,10032,8800,2144,64,13,596,6028,20064,24112,9536,832,14
%N A207623 Triangle of coefficients of polynomials v(n,x) jointly generated with A207622; see the Formula section.
%C A207623 Column n is divisible by 2^(n-1); row n ends with 2^(n-1).
%C A207623 Column 2: 2*A004006.
%F A207623 u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=2x*u(n-1,x)+v(n-1,x)+1, where u(1,x)=1, v(1,x)=1.
%e A207623 First five rows:
%e A207623 1
%e A207623 2...2
%e A207623 3...6
%e A207623 4...14...4
%e A207623 5...28...20
%t A207623 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207623 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207623 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1
%t A207623 Table[Factor[u[n, x]], {n, 1, z}]
%t A207623 Table[Factor[v[n, x]], {n, 1, z}]
%t A207623 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207623 TableForm[cu]
%t A207623 Flatten[%]    (* A207622 *)
%t A207623 Table[Expand[v[n, x]], {n, 1, z}]
%t A207623 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207623 TableForm[cv]
%t A207623 Flatten[%]    (* A207623 *)
%Y A207623 Cf. A207622.
%K A207623 nonn,tabl
%O A207623 1,2
%A A207623 _Clark Kimberling_, Feb 20 2012