cp's OEIS Frontend

A111548 Matrix inverse of triangle A111544.

%I A111548 #7 Jun 13 2017 22:32:23
%S A111548 1,-1,1,-3,-2,1,-15,-3,-3,1,-99,-15,-3,-4,1,-783,-99,-15,-3,-5,1,
%T A111548 -7083,-783,-99,-15,-3,-6,1,-71415,-7083,-783,-99,-15,-3,-7,1,-789939,
%U A111548 -71415,-7083,-783,-99,-15,-3,-8,1,-9485343,-789939,-71415,-7083,-783,-99,-15,-3,-9,1,-122721723,-9485343,-789939,-71415
%N A111548 Matrix inverse of triangle A111544.
%C A111548 The column sequences are all equal after the initial terms and are derived from the logarithm of a factorial series (cf. A111546).
%F A111548 T(n, n)=1 and T(n+1, n)=-n-1, else T(n+k+1, k) = -A111546(k) for k>=1.
%e A111548 Triangle begins:
%e A111548 1;
%e A111548 -1,1;
%e A111548 -3,-2,1;
%e A111548 -15,-3,-3,1;
%e A111548 -99,-15,-3,-4,1;
%e A111548 -783,-99,-15,-3,-5,1;
%e A111548 -7083,-783,-99,-15,-3,-6,1;
%e A111548 -71415,-7083,-783,-99,-15,-3,-7,1;
%e A111548 -789939,-71415,-7083,-783,-99,-15,-3,-8,1; ...
%o A111548 (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+2)!/2!*x^i)),n-k-1))))
%Y A111548 Cf. A111544, A111546, A111540.
%K A111548 sign,tabl
%O A111548 0,4
%A A111548 _Paul D. Hanna_, Aug 07 2005