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%I #7 Feb 19 2015 14:20:53
%S 1,2,8,43,265,1832,14160,121771,1157557,12080436,137505288,1696841395,
%T 22578385961,322377704664,4917809053032,79840791037379,
%U 1374705370985669,25024307510421060,480230285880218992
%N Q-residue of the triangle A094727, where Q=Pascal's triangle. (See Comments.)
%C For the definition of Q-residue, see A193649.
%F Conjecture: a(n) +(-n-5)*a(n-1) +2*(2*n+1)*a(n-2) +(-5*n+8)*a(n-3) +2*(n-3)
%F *a(n-4)=0. - _R. J. Mathar_, Feb 19 2015
%t q[n_, k_] := n + k + 1;(* A094727 *)
%t r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}]
%t p[n_, k_] := n!/(k! (n - k)!); (* Pascal's triangle *)
%t v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
%t Table[v[n], {n, 0, 18}] (* A193659 *)
%t TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
%t Table[r[k], {k, 0, 8}] (* A193668 *)
%t TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]
%Y Cf. A193668, A094727, A193649.
%K nonn
%O 0,2
%A _Clark Kimberling_, Aug 02 2011
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