%I #3 Mar 31 2012 13:20:05
%S 0,1,5,20,45,25,240,350,600,250,3000,9250,13125,8750,1875,93000,
%T 373750,361875,240625,103125,15625,3690000,11077500,12818750,8531250,
%U 4156250,1181250,125000,116550000,312037500
%N Triangle of coefficients of polynomials (rising powers) useful for convolutions of A000032(n+1), n >= 0 (Lucas numbers).
%C The row polynomials pL1(n,x) := sum(a(n,m)*x^m,m=0..n) and pL2(n,x) := sum(A061189(n,m)*x^m,m=0..n) appear in the k-fold convolution of the Lucas numbers L(n+1)= A000204(n+1)= A000032(n+1), n >= 0, as follows: L(k; n) := A060922(n+k,k)= (pL1(k,n)*L(n+2)+pL2(k,n)*L(n+1)/(k!*5^k).
%e {0}; {1,5}; {20,45,25}; {240,350,600,250}; ...; pL1(2,n)=5*(4+9*n+5*n^2)= 5*(1+n)*(4+5*n).
%Y A061189(n, m) (companion triangle), A060922(n, m) (Lucas convolution triangle).
%K nonn,tabl
%O 0,3
%A _Wolfdieter Lang_, Apr 20 2001