%I
%S 0,1,0,4,1,0,15,5,1,0,64,23,6,1,0,325,119,33,7,1,0,1956,719,202,45,8,
%T 1,0,13699,5039,1419,319,59,9,1,0,109600,40319,11358,2557,476,75,10,1,
%U 0,986409,362879,102229,23019,4289,679,93,11,1,0,9864100,3628799,1022298
%N Triangle read by rows of T(n,k)=n*T(n1,k)+nk starting at T(n,n)=0.
%C Taking the triangle into negative values of n and k would produce results close to (k+1)*e*n!  1, i.e. one less than multiples of A000522 for nonnegative n.
%F For k>0, T(n, k)=ceiling[ (A001339(k1)/(k1)!  (k1)*e) *n!  1] where A001339(k1)=ceiling[(k1)!*(k1)*e for k>1]. T(n, 0)=floor[e*n!  1] for n>0; T(n, 1)=n!1. T(n, n)=0; T(n, n1)=n+2; T(n, n2)=n^2+3n+5=A027688(n+1).
%e Rows start: 0; 1,0; 4,1,0; 15,5,1,0; 64,23,6,1,0; 325,119,33,7,1,0; etc.
%Y Columns include A007526 and A033312.
%K nonn,tabl
%O 0,4
%A _Henry Bottomley_, Apr 16 2003
