A107726 - OEIS

A107726

Matrix inverse of triangle A107717, read by rows.

1, -3, 1, -3, -6, 1, -21, -3, -9, 1, -219, -21, -3, -12, 1, -2973, -219, -21, -3, -15, 1, -49323, -2973, -219, -21, -3, -18, 1, -964173, -49323, -2973, -219, -21, -3, -21, 1, -21680571, -964173, -49323, -2973, -219, -21, -3, -24, 1, -551173053, -21680571, -964173, -49323, -2973, -219, -21, -3, -27, 1

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OFFSET

0,2

COMMENTS

Except for initial terms, each column is the same and equals negative A107716 (inverse INVERT of triple factorials).

LINKS

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

EXAMPLE

Triangle begins:

-3,1;

-3,-6,1;

-21,-3,-9,1;

-219,-21,-3,-12,1;

-2973,-219,-21,-3,-15,1;

-49323,-2973,-219,-21,-3,-18,1;

-964173,-49323,-2973,-219,-21,-3,-21,1; ...

Matrix inverse is A107717:

3,1;

21,6,1;

219,57,9,1;

2973,723,111,12,1;

49323,11361,1713,183,15,1; ...

PROG

(PARI) T(n, k)=if(n<k || k<0, 0, matrix(n+1, n+1, m, j, if(m>=j, if(m==j, 1, if(m==j+1, -3*j, polcoeff(1/sum(i=0, m-j, prod(r=0, i-1, 3*r+1)*x^i)+O(x^m), m-j)))))[n+1, k+1])

CROSSREFS

Cf. A107716, A107717.

Sequence in context: A181425 A174505 A096713 * A114159 A236560 A291723

Adjacent sequences: A107723 A107724 A107725 * A107727 A107728 A107729

KEYWORD

sign,tabl

AUTHOR

Paul D. Hanna, May 30 2005

STATUS

approved