The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A111540

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A111540

Matrix inverse of triangle A111536.
(history; published version)

#6 by Charles R Greathouse IV at Tue Jun 13 22:31:43 EDT 2017

STATUS

editing

approved

#5 by Charles R Greathouse IV at Tue Jun 13 22:31:37 EDT 2017

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))))}

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 18:36:50 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Aug 06 2005

Discussion

Fri Mar 30

18:36

OEIS Server: https://oeis.org/edit/global/213

#3 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

KEYWORD

sign,tabl,new

AUTHOR

Paul D . Hanna (pauldhanna(AT)juno.com), Aug 06 2005

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

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

KEYWORD

sign,tabl,new

#1 by N. J. A. Sloane at Wed Sep 21 03:00:00 EDT 2005

NAME

Matrix inverse of triangle A111536.

DATA

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).

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.

KEYWORD

sign,tabl

AUTHOR

Paul D Hanna (pauldhanna(AT)juno.com), Aug 06 2005

STATUS

approved