%I #4 Mar 31 2012 13:20:04

%S 2,5,17,15,120,225,50,700,3050,4080,175,3775,28625,89225,94440,625,

%T 19225,223175,1208975,3006000,2666880,2250,93500,1537100,12689800,

%U 54824650,115299900,89016480,8125,438250,9670750,112454500,737744125

%N Coefficient triangle of polynomials (falling powers) related to Fibonacci convolutions. Companion triangle to A057281.

%C The row polynomials are q(k,x) := sum(a(k,m)*x^(k-m),m=0..k), k=0,1,2,..

%C The k-th convolution of F0(n) := A000045(n+1), n >= 0, (Fibonacci numbers starting with F0(0)=1) with itself is Fk(n) := A037027(n+k,k) = (p(k-1,n)*(n+1)*F0(n+1) + q(k-1,n)*(n+2)*F0(n))/(k!*5^k), k=1,2,..., where the companion polynomials p(k,n) := sum(b(k,m)*n^(k-m),m=0..k) are the row polynomials of triangle b(k,m)= A057281(k,m).

%C a(k,0)= A020876(k), k >= 0.

%e k=2: F2(n)=((5*n^2+21*n+16)*F(n+2)+(5*n^2+27*n+34)*F(n+1))/50, F(n) := A000045(n); see A001628.

%e 2; 5,17; 15,120,225; 50,700,3050,4080; 175,3775,28625,89225,94440; ...

%Y Cf. A000045, A037027, A057995, A057280, A057281.

%Y Row sums: A151615.

%K nonn,tabl

%O 1,1

%A _Wolfdieter Lang_, Sep 13 2000