A111540 Matrix inverse of triangle A111536.

1, -1, 1, -2, -2, 1, -8, -2, -3, 1, -44, -8, -2, -4, 1, -296, -44, -8, -2, -5, 1, -2312, -296, -44, -8, -2, -6, 1, -20384, -2312, -296, -44, -8, -2, -7, 1, -199376, -20384, -2312, -296, -44, -8, -2, -8, 1, -2138336, -199376, -20384, -2312, -296, -44, -8, -2, -9, 1, -24936416, -2138336, -199376, -20384, -2312, -296

Offset

0,4

Comments

The column sequences are derived from the logarithm of a factorial series (cf. A111537).

Links

Table of n, a(n) for n=0..60.

Formula

T(n, n)=1 and T(n+1, n)=n+1, else T(n+k+1, k) = -A111537(k) for k>=1.

Example

Triangle begins:
1;
-1,1;
-2,-2,1;
-8,-2,-3,1;
-44,-8,-2,-4,1;
-296,-44,-8,-2,-5,1;
-2312,-296,-44,-8,-2,-6,1;
-20384,-2312,-296,-44,-8,-2,-7,1;
-199376,-20384,-2312,-296,-44,-8,-2,-8,1; ...
After initial terms, all columns are equal to -A111537.

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, (i+1)!/1!*x^i)), n-k-1))))

Crossrefs

Cf. A111536, A111537.

Sequence in context: A225925 A357553 A246745 * A360410 A346709 A096440

Adjacent sequences: A111537 A111538 A111539 * A111541 A111542 A111543

Keyword

sign,tabl

Author

Paul D. Hanna, Aug 06 2005

Status

approved