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A194007 Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers) and q(n,x)=x*q(n-1,x)+n+1, with q(0,x)=1.

%I A194007 #7 Mar 30 2012 18:57:39
%S A194007 1,2,5,3,8,14,5,13,23,34,8,21,37,55,74,13,34,60,89,120,152,21,55,97,
%T A194007 144,194,246,299,34,89,157,233,314,398,484,571,55,144,254,377,508,644,
%U A194007 783,924,1066,89,233,411,610,822,1042,1267,1495,1725,1956,144,377
%N A194007 Triangular array:  the fission of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers) and q(n,x)=x*q(n-1,x)+n+1, with q(0,x)=1.
%C A194007 See A193842 for the definition of the fission of P by Q, where P and Q are sequences of polynomials or triangular arrays (of coefficients of polynomials).
%e A194007 First six rows:
%e A194007 1
%e A194007 2....5
%e A194007 3....8....14
%e A194007 5....13...23...34
%e A194007 8....21...37...55...74
%e A194007 13...34...60...89...120...152
%t A194007 z = 11;
%t A194007 p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}];
%t A194007 q[n_, x_] := x*q[n - 1, x] + n + 1; q[0, n_] := 1;
%t A194007 p1[n_, k_] := Coefficient[p[n, x], x^k];
%t A194007 p1[n_, 0] := p[n, x] /. x -> 0;
%t A194007 d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}]
%t A194007 h[n_] := CoefficientList[d[n, x], {x}]
%t A194007 TableForm[Table[Reverse[h[n]], {n, 0, z}]]
%t A194007 Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A194007 *)
%t A194007 TableForm[Table[h[n], {n, 0, z}]]
%t A194007 Flatten[Table[h[n], {n, -1, z}]]  (* A194008 *)
%Y A194007 Cf. A193842, A194008.
%K A194007 nonn,tabl
%O A194007 0,2
%A A194007 _Clark Kimberling_, Aug 11 2011