%I #5 Mar 30 2012 18:57:39
%S 1,1,2,2,5,8,3,8,14,23,5,13,23,39,63,8,21,37,63,103,167,13,34,60,102,
%T 167,272,440,21,55,97,165,270,440,713,1154,34,89,157,267,437,712,1154,
%U 1869,3024,55,144,254,432,707,1152,1867,3024,4894,7919,89,233
%N Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{F(k+2)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).
%C See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays. The first five rows of P, from the coefficients of p(n,k):
%C 1
%C 1...2
%C 1...2...3
%C 1...2...3...5
%C 1...2...3...5...8
%e First six rows of A193906:
%e 1
%e 1...2
%e 2...5....8
%e 3...8....14...23
%e 5...13...23...39...63
%e 8...21...37...63...103...167
%t z = 12;
%t p[n_, x_] := Sum[Fibonacci[k + 2]*x^(n - k), {k, 0, n}];
%t q[n_, x_] := p[n, x]
%t t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0;
%t w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
%t g[n_] := CoefficientList[w[n, x], {x}]
%t TableForm[Table[Reverse[g[n]], {n, -1, z}]]
%t Flatten[Table[Reverse[g[n]], {n, -1, z}]] (* A193906 *)
%t TableForm[Table[g[n], {n, -1, z}]]
%t Flatten[Table[g[n], {n, -1, z}]] (* A193907 *)
%Y Cf. A193722, A193907.
%K nonn,tabl
%O 0,3
%A _Clark Kimberling_, Aug 08 2011