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

%I A207622 #15 Dec 25 2022 13:59:11
%S A207622 1,2,4,2,7,8,11,22,4,16,50,24,22,100,88,8,29,182,252,64,37,308,616,
%T A207622 296,16,46,492,1344,1032,160,56,750,2688,3000,896,32,67,1100,5016,
%U A207622 7656,3696,384,79,1562,8844,17688,12496,2528,64,92,2158,14872,37752
%N A207622 Triangle of coefficients of polynomials u(n,x) jointly generated with A207623; see the Formula section.
%C A207622 With offset 0, equals the stretched Riordan array ((1 - z + z^2)/(1 - z)^3, 2*z^2/(1 - z)^2) in the notation of Corsani et al., Section 2. Cf. A207616. - _Peter Bala_, Dec 31 2015
%H A207622 C. Corsani, D. Merlini, and R. Sprugnoli, <a href="http://dx.doi.org/10.1016/S0012-365X(97)00110-6">Left-inversion of combinatorial sums</a>, Discrete Mathematics, 180 (1998) 107-122.
%F A207622 u(n,x) = u(n-1,x) + v(n-1,x), v(n,x) = 2*x*u(n-1,x) + v(n-1,x) + 1, where u(1,x) = 1, v(1,x) = 1.
%e A207622 First five rows:
%e A207622    1
%e A207622    2
%e A207622    4  2
%e A207622    7  8
%e A207622   11 22  4
%t A207622 u[1, x_] := 1; v[1, x_] := 1; z = 16;
%t A207622 u[n_, x_] := u[n - 1, x] + v[n - 1, x]
%t A207622 v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1
%t A207622 Table[Factor[u[n, x]], {n, 1, z}]
%t A207622 Table[Factor[v[n, x]], {n, 1, z}]
%t A207622 cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
%t A207622 TableForm[cu]
%t A207622 Flatten[%]    (* A207622 *)
%t A207622 Table[Expand[v[n, x]], {n, 1, z}]
%t A207622 cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
%t A207622 TableForm[cv]
%t A207622 Flatten[%]    (* A207623 *)
%Y A207622 Cf. A207623, A207616, A208510, A000124 (column 1).
%K A207622 nonn,tabf,easy
%O A207622 1,2
%A A207622 _Clark Kimberling_, Feb 20 2012