%I #3 Mar 30 2012 18:36:50
%S 0,3,8,36,212,1496,12128,110288,1108064,12171872,145061120,1864321472,
%T 25710635648,378871778432,5943632568320,98936446059776,
%U 1742232571097600,32367994818881024,632845309575139328,12991224275641441280
%N Column 2 of triangle A111541, which is the matrix logarithm of A111536.
%o (PARI) {a(n)=local(M=matrix(n+3,n+3,m,j,if(m==j,1,if(m==j+1,-m+1, -(m-j-1)*polcoeff(log(sum(i=0,m,(i+1)!/1!*x^i)),m-j-1))))); if(n<0,0,sum(i=1,#M,(M^0-M)^i/i)[n+3,3])}
%Y Cf. A111541 (triangle), A111538 (column 0), A111542 (column 1), A111536.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Aug 06 2005