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A193664 Q-residue of A049310 (triangle of coefficients of Fibonacci polynomials), where Q=Pascal's triangle. (See Comments.)

%I A193664 #5 Mar 30 2012 18:57:38
%S A193664 0,1,1,6,11,68,177,1215,4059,30733,124408,1027972,4862600,43450761,
%T A193664 234283662,2247091674,13563976285,138780931929,925063455844,
%U A193664 10044476018973,73144254450840,839146997933059,6618306039456419
%N A193664 Q-residue of A049310 (triangle of coefficients of Fibonacci polynomials), where Q=Pascal's triangle.  (See Comments.)
%C A193664 The definition of Q-residue is given at A193649.
%t A193664 f[n_, x_] := Fibonacci[n, x];
%t A193664 q[n_, k_] := Coefficient[(x + 1)^n, x, k]; (* Pascal's triangle *)
%t A193664 r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];
%t A193664 p[n_, k_] := Coefficient[f[n, x], x, k];
%t A193664 v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
%t A193664 Table[v[n], {n, 0, 22}]    (* A193664 *)
%t A193664 TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
%t A193664 Table[r[k], {k, 0, 8}]  (* A000110 *)
%t A193664 TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]
%Y A193664 Cf. A049310, A193649, A000110.
%K A193664 nonn
%O A193664 0,4
%A A193664 _Clark Kimberling_, Aug 02 2011