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Search: id:A111941
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| A111941 |
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Matrix log of triangle A111940, which shifts columns left and up under matrix inverse; these terms are the result of multiplying each element in row n and column k by (n-k)!. |
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+0
7
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| 0, 1, 0, -1, -1, 0, 1, 1, 1, 0, -2, -1, -1, -1, 0, 4, 2, 1, 1, 1, 0, -12, -4, -2, -1, -1, -1, 0, 36, 12, 4, 2, 1, 1, 1, 0, -144, -36, -12, -4, -2, -1, -1, -1, 0, 576, 144, 36, 12, 4, 2, 1, 1, 1, 0, -2880, -576, -144, -36, -12, -4, -2, -1, -1, -1, 0, 14400, 2880, 576, 144, 36, 12, 4, 2, 1, 1, 1, 0, -86400, -14400, -2880, -576, -144, -36
(list; table; graph; listen)
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OFFSET
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0,11
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FORMULA
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T(n, k) = (-1)^k*T(n-k, 0) = (-1)^k*A111942(n-k) for n>=k>=0.
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EXAMPLE
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Matrix log of A111940, with factorial denominators, begins:
0;
1/1!, 0;
-1/2!, -1/1!, 0;
1/3!, 1/2!, 1/1!, 0;
-2/4!, -1/3!, -1/2!, -1/1!, 0;
4/5!, 2/4!, 1/3!, 1/2!, 1/1!, 0;
-12/6!, -4/5!, -2/4!, -1/3!, -1/2!, -1/1!, 0; ...
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PROGRAM
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(PARI) {T(n, k, q=-1)=local(A=Mat(1), B); if(n<k|k<0, 0, for(m=1, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, if(j==1, B[i, j]=(A^q)[i-1, 1], B[i, j]=(A^q)[i-1, j-1])); )); A=B); B=sum(i=1, #A, -(A^0-A)^i/i); return((n-k)!*B[n+1, k+1]))}
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CROSSREFS
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Cf. A111940 (triangle), A111942 (column 0), A110504 (variant).
Sequence in context: A089339 A127284 A120691 this_sequence A153462 A126310 A109086
Adjacent sequences: A111938 A111939 A111940 this_sequence A111942 A111943 A111944
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KEYWORD
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frac,sign,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 23 2005
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