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A193661 Q-residue of the triangle A193673, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)

%I A193661 #8 Feb 19 2015 14:22:18
%S A193661 1,3,15,93,621,4263,29595,206433,1442841,10093323,70633575,494375973,
%T A193661 3460454661,24222651183,169556963955,1186893964713,8308243404081,
%U A193661 58157660781843,407103496332735,2849724086908653,19948067446099101
%N A193661 Q-residue of the triangle A193673, where Q is the triangular array (t(i,j)) given by t(i,j)=1.  (See Comments.)
%C A193661 See A193649 for the definition of Q-residue.
%F A193661 Conjecture: G.f.: ( -1+8*x-13*x^2 ) / ( (x-1)*(3*x-1)*(7*x-1) ). - _R. J. Mathar_, Feb 19 2015
%t A193661 q[n_, k_] := 1; r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}]
%t A193661 p[n_, k_] := Coefficient[(1/2) ((x + 3)^n + (x + 1)^n), x, k] (* A193673 *)
%t A193661 v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
%t A193661 Table[v[n], {n, 0, 20}]    (* A193661 *)
%t A193661 TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
%t A193661 Table[r[k], {k, 0, 8}]  (* 2^k *)
%t A193661 TableForm[Table[p[n, k], {n, 0, 10}, {k, 0, n}]] (* A193673 as a triangle *)
%t A193661 Flatten[%] (* A193673 as a sequence *)
%Y A193661 Cf. A193649, A193673.
%K A193661 nonn
%O A193661 0,2
%A A193661 _Clark Kimberling_, Aug 02 2011