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%I #3 Mar 31 2012 13:20:04
%S 2,17,5,225,120,15,4080,3050,700,50,94440,89225,28625,3775,175,
%T 2666880,3006000,1208975,223175,19225,625,89016480,115299900,54824650,
%U 12689800,1537100,93500,2250,3430929600,4973077800,2695596850,737744125
%N Coefficient triangle of polynomials (rising powers) related to Fibonacci convolutions. Companion triangle to A057995.
%C The row polynomials are q(k,x) := sum(a(k,m)*x^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^m,m=0..k), k >= 0, are the row polynomials of triangle b(k,m)= A057995(k,m).
%e k=2: F2(n)=((16+5*n)*(n+1)*F0(n+1)+(17+5*n)*(n+2)*F0(n))/50, cf. A001628.
%Y Cf. A000045, A037027, A057995.
%K nonn,tabl
%O 0,1
%A _Wolfdieter Lang_, Sep 13 2000
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