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%I #3 Mar 30 2012 18:36:50
%S 0,1,0,5,2,0,34,7,3,0,282,44,10,4,0,2696,354,60,14,5,0,28792,3328,470,
%T 84,19,6,0,337072,35144,4344,654,118,25,7,0,4273632,407984,45320,6008,
%U 936,164,32,8,0,58195072,5137824,521200,62344,8704,1352,224,40,9,0
%N Matrix logarithm of triangle A111553.
%e Triangle begins:
%e 0;
%e 1,0;
%e 5,2,0;
%e 34,7,3,0;
%e 282,44,10,4,0;
%e 2696,354,60,14,5,0;
%e 28792,3328,470,84,19,6,0;
%e 337072,35144,4344,654,118,25,7,0;
%e 4273632,407984,45320,6008,936,164,32,8,0; ...
%o (PARI) {T(n,k)=local(M=matrix(n+2,n+2,m,j,if(m==j,1,if(m==j+1,-m+1, -(m-j-1)*polcoeff(log(sum(i=0,m,(i+3)!/3!*x^i)),m-j-1))))); sum(i=1,#M,(M^0-M)^i/i)[n+1,k+1]}
%Y Cf. A111553, A111557, A104986, A111541, A111549.
%K nonn,tabl
%O 0,4
%A _Paul D. Hanna_, Aug 07 2005
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