

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, (nk1)*polcoeff(log(sum(i=0, n, (i+1)!/1!*x^i)), nk1))))


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



