cp's OEIS Frontend

A111540 Matrix inverse of triangle A111536.

%I A111540 #6 Jun 13 2017 22:31:43
%S A111540 1,-1,1,-2,-2,1,-8,-2,-3,1,-44,-8,-2,-4,1,-296,-44,-8,-2,-5,1,-2312,
%T A111540 -296,-44,-8,-2,-6,1,-20384,-2312,-296,-44,-8,-2,-7,1,-199376,-20384,
%U A111540 -2312,-296,-44,-8,-2,-8,1,-2138336,-199376,-20384,-2312,-296,-44,-8,-2,-9,1,-24936416,-2138336,-199376,-20384,-2312,-296
%N A111540 Matrix inverse of triangle A111536.
%C A111540 The column sequences are derived from the logarithm of a factorial series (cf. A111537).
%F A111540 T(n, n)=1 and T(n+1, n)=n+1, else T(n+k+1, k) = -A111537(k) for k>=1.
%e A111540 Triangle begins:
%e A111540 1;
%e A111540 -1,1;
%e A111540 -2,-2,1;
%e A111540 -8,-2,-3,1;
%e A111540 -44,-8,-2,-4,1;
%e A111540 -296,-44,-8,-2,-5,1;
%e A111540 -2312,-296,-44,-8,-2,-6,1;
%e A111540 -20384,-2312,-296,-44,-8,-2,-7,1;
%e A111540 -199376,-20384,-2312,-296,-44,-8,-2,-8,1; ...
%e A111540 After initial terms, all columns are equal to -A111537.
%o A111540 (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,(i+1)!/1!*x^i)),n-k-1))))
%Y A111540 Cf. A111536, A111537.
%K A111540 sign,tabl
%O A111540 0,4
%A A111540 _Paul D. Hanna_, Aug 06 2005