A111548 - OEIS

%I #7 Jun 13 2017 22:32:23

%S 1,-1,1,-3,-2,1,-15,-3,-3,1,-99,-15,-3,-4,1,-783,-99,-15,-3,-5,1,

%T -7083,-783,-99,-15,-3,-6,1,-71415,-7083,-783,-99,-15,-3,-7,1,-789939,

%U -71415,-7083,-783,-99,-15,-3,-8,1,-9485343,-789939,-71415,-7083,-783,-99,-15,-3,-9,1,-122721723,-9485343,-789939,-71415

%N Matrix inverse of triangle A111544.

%C The column sequences are all equal after the initial terms and are derived from the logarithm of a factorial series (cf. A111546).

%F T(n, n)=1 and T(n+1, n)=-n-1, else T(n+k+1, k) = -A111546(k) for k>=1.

%e Triangle begins:

%e 1;

%e -1,1;

%e -3,-2,1;

%e -15,-3,-3,1;

%e -99,-15,-3,-4,1;

%e -783,-99,-15,-3,-5,1;

%e -7083,-783,-99,-15,-3,-6,1;

%e -71415,-7083,-783,-99,-15,-3,-7,1;

%e -789939,-71415,-7083,-783,-99,-15,-3,-8,1; ...

%o (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 Cf. A111544, A111546, A111540.

%K sign,tabl

%O 0,4

%A _Paul D. Hanna_, Aug 07 2005