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Search: id:A110504
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| A110504 |
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Triangle, read by rows, which equals the matrix logarithm of the triangle A110503. |
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+0
11
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| 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
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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The unsigned columns this triangle are all equal to A110505. Triangle A110503 shifts one column left under matrix inverse.
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FORMULA
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T(n, k) = (-1)^k*A110505(n-k).
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EXAMPLE
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Triangle begins:
0;
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;
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; ...
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PROGRAM
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(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]}
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CROSSREFS
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Cf. A110503 (matrix exponential), A110505 (unsigned columns).
Sequence in context: A074678 A130888 A010601 this_sequence A111246 A143395 A090536
Adjacent sequences: A110501 A110502 A110503 this_sequence A110505 A110506 A110507
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KEYWORD
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sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 23 2005
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