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A193665 Q-residue of A075392, where Q=A075392. (See Comments.)

%I A193665 #10 Feb 19 2015 14:26:10
%S A193665 1,6,33,208,1505,12330,112973,1145568,12742389,154308350,2021296189,
%T A193665 28480485024,429565218277,6905903216562,117891260108985,
%U A193665 2129869055824000,40600135597843817,814383095809997142,17147155400516728601,378137512431282658800
%N A193665 Q-residue of A075392, where Q=A075392.  (See Comments.)
%C A193665 The definition of Q-residue is given at A193649.
%F A193665 Conjecture: a(n) +(-n-4)*a(n-1) +(n+1)*a(n-2) -a(n-3)=0. - _R. J. Mathar_, Feb 19 2015
%t A193665 q[n_, k_] := (k + 1) (n + 1);  (* A075362 *)
%t A193665 r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];
%t A193665 p[n_, k_] := (k + 1) (n + 1);  (* A075362 *)
%t A193665 v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
%t A193665 Table[v[n], {n, 0, 20}]    (* A193665 *)
%t A193665 TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
%t A193665 Table[r[k], {k, 0, 8}]  (* A193665 *)
%t A193665 TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]
%Y A193665 Cf. A075362, A193649.
%K A193665 nonn
%O A193665 0,2
%A A193665 _Clark Kimberling_, Aug 02 2011