A111548 Matrix inverse of triangle A111544.

1, -1, 1, -3, -2, 1, -15, -3, -3, 1, -99, -15, -3, -4, 1, -783, -99, -15, -3, -5, 1, -7083, -783, -99, -15, -3, -6, 1, -71415, -7083, -783, -99, -15, -3, -7, 1, -789939, -71415, -7083, -783, -99, -15, -3, -8, 1, -9485343, -789939, -71415, -7083, -783, -99, -15, -3, -9, 1, -122721723, -9485343, -789939, -71415

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..58.

Formula

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

Example

Triangle begins:
1;
-1,1;
-3,-2,1;
-15,-3,-3,1;
-99,-15,-3,-4,1;
-783,-99,-15,-3,-5,1;
-7083,-783,-99,-15,-3,-6,1;
-71415,-7083,-783,-99,-15,-3,-7,1;
-789939,-71415,-7083,-783,-99,-15,-3,-8,1; ...

Prog

(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))))

Crossrefs

Cf. A111544, A111546, A111540.

Sequence in context: A152400 A291978 A342217 * A140709 A109282 A135902

Adjacent sequences: A111545 A111546 A111547 * A111549 A111550 A111551

Keyword

sign,tabl

Author

Paul D. Hanna, Aug 07 2005

Status

approved