cp's OEIS Frontend

A111559 Matrix inverse of triangle A111553.

%I A111559 #6 Jun 13 2017 22:32:42
%S A111559 1,-1,1,-4,-2,1,-24,-4,-3,1,-184,-24,-4,-4,1,-1664,-184,-24,-4,-5,1,
%T A111559 -17024,-1664,-184,-24,-4,-6,1,-192384,-17024,-1664,-184,-24,-4,-7,1,
%U A111559 -2366144,-192384,-17024,-1664,-184,-24,-4,-8,1,-31362304,-2366144,-192384,-17024,-1664,-184,-24,-4,-9,1
%N A111559 Matrix inverse of triangle A111553.
%C A111559 After initial terms, all columns are equal to -A111556.
%F A111559 T(n, n)=1 and T(n+1, n)=-n-1, else T(n+k+1, k) = -A111556(k) for k>=1.
%e A111559 Triangle begins:
%e A111559 1;
%e A111559 -1,1;
%e A111559 -4,-2,1;
%e A111559 -24,-4,-3,1;
%e A111559 -184,-24,-4,-4,1;
%e A111559 -1664,-184,-24,-4,-5,1;
%e A111559 -17024,-1664,-184,-24,-4,-6,1;
%e A111559 -192384,-17024,-1664,-184,-24,-4,-7,1; ...
%o A111559 (PARI) T(n,k)=if(n<k || k<0,0,if(n==k,1,if(n==k+1,-n, -(n-k-1)*polcoeff(log(sum(i=0,n-k,(i+3)!/3!*x^i)),n-k-1))))
%Y A111559 Cf. A111553, A111556, A104984, A111540, A111548.
%K A111559 sign,tabl
%O A111559 0,4
%A A111559 _Paul D. Hanna_, Aug 07 2005