|
%I #3 Mar 31 2012 13:20:04
%S 1,5,16,20,160,300,75,1075,4850,6840,275,6100,48175,159650,186120,
%T 1000,31550,379700,2168650,5846700,5916240,3625,153875,2605175,
%U 22426825,103057800,238437900,215717040,13125,720375,16273875,195469125
%N Coefficient triangle of polynomials (falling powers) related to Fibonacci convolutions. Companion triangle to A057282.
%C The row polynomials are p(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 q(k,n) := sum(b(k,m)*n^(k-m),m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A057282(k,m).
%C a(k,0)= A030191(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.
%Y Cf. A000045, A037027, A057995, A057280, A057282.
%K nonn,tabl
%O 0,2
%A _Wolfdieter Lang_, Sep 13 2000
|
