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A207615 Triangle of coefficients of polynomials v(n,x) jointly generated with A207614; see the Formula section.

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