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A111548 Matrix inverse of triangle A111544. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified January 29 09:12 EST 2022. Contains 350672 sequences. (Running on oeis4.)