A110504 - OEIS

A110504

Triangle, read by rows, which equals the matrix logarithm of the triangle A110503.

0, 1, 0, 3, -1, 0, 7, -3, 1, 0, 30, -7, 3, -1, 0, 144, -30, 7, -3, 1, 0, 876, -144, 30, -7, 3, -1, 0, 6084, -876, 144, -30, 7, -3, 1, 0, 48816, -6084, 876, -144, 30, -7, 3, -1, 0, 438624, -48816, 6084, -876, 144, -30, 7, -3, 1, 0, 4389120, -438624, 48816, -6084, 876, -144, 30, -7, 3, -1, 0

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OFFSET

0,4

COMMENTS

The unsigned columns this triangle are all equal to A110505. Triangle A110503 shifts one column left under matrix inverse.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n, k) = (-1)^k*A110505(n-k).

EXAMPLE

Triangle begins:

1/1!, 0;

3/2!, -1/1!, 0;

7/3!, -3/2!, 1/1!, 0;

30/4!, -7/3!, 3/2!, -1/1!, 0;

144/5!, -30/4!, 7/3!, -3/2!, 1/1!, 0;

876/6!, -144/5!, 30/4!, -7/3!, 3/2!, -1/1!, 0;

6084/7!, -876/6!, 144/5!, -30/4!, 7/3!, -3/2!, 1/1!, 0; ...

Unsigned columns all equal A110505.

Exponential function of matrix equals A110503:

1,1;

1,-1,1;

1,-2,1,1;

1,-1,1,-1,1;

1,-1,1,-2,1,1;

1,-1,1,-1,1,-1,1;

1,-1,1,-1,1,-2,1,1; ...

PROG

(PARI) T(n, k)=local(M=matrix(n+1, n+1, r, c, if(r>=c, if(r==c || c%2==1, 1, if(r%2==0 && r==c+2, -2, -1))))); sum(i=1, #M, -(M^0-M)^i/i)[n+1, k+1]

CROSSREFS

Cf. A110503 (matrix exponential), A110505 (unsigned columns).

Sequence in context: A130888 A010601 A176108 * A378329 A361475 A111246

Adjacent sequences: A110501 A110502 A110503 * A110505 A110506 A110507

KEYWORD

sign,tabl

AUTHOR

Paul D. Hanna, Jul 23 2005

STATUS

approved