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A111540 Matrix inverse of triangle A111536. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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: A100632 A225925 A246745 * A096440 A181738 A121350

Adjacent sequences:  A111537 A111538 A111539 * A111541 A111542 A111543

KEYWORD

sign,tabl

AUTHOR

Paul D. Hanna, Aug 06 2005

STATUS

approved

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Last modified December 18 18:49 EST 2018. Contains 318243 sequences. (Running on oeis4.)