A111559 Matrix inverse of triangle A111553.

1, -1, 1, -4, -2, 1, -24, -4, -3, 1, -184, -24, -4, -4, 1, -1664, -184, -24, -4, -5, 1, -17024, -1664, -184, -24, -4, -6, 1, -192384, -17024, -1664, -184, -24, -4, -7, 1, -2366144, -192384, -17024, -1664, -184, -24, -4, -8, 1, -31362304, -2366144, -192384, -17024, -1664, -184, -24, -4, -9, 1

Offset

0,4

Comments

After initial terms, all columns are equal to -A111556.

Links

Table of n, a(n) for n=0..54.

Formula

T(n, n)=1 and T(n+1, n)=-n-1, else T(n+k+1, k) = -A111556(k) for k>=1.

Example

Triangle begins:
1;
-1,1;
-4,-2,1;
-24,-4,-3,1;
-184,-24,-4,-4,1;
-1664,-184,-24,-4,-5,1;
-17024,-1664,-184,-24,-4,-6,1;
-192384,-17024,-1664,-184,-24,-4,-7,1; ...

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+3)!/3!*x^i)), n-k-1))))

Crossrefs

Cf. A111553, A111556, A104984, A111540, A111548.

Sequence in context: A144088 A039948 A111536 * A224798 A239894 A152406

Adjacent sequences: A111556 A111557 A111558 * A111560 A111561 A111562

Keyword

sign,tabl

Author

Paul D. Hanna, Aug 07 2005

Status

approved