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Search: id:A111813
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| A111813 |
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Matrix log of triangle A078121, which shifts columns left and up under matrix square; these terms are the result of multiplying each element in row n and column k by (n-k)!. |
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+0
9
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| 0, 1, 0, 0, 2, 0, -2, 0, 4, 0, 0, -4, 0, 8, 0, 216, 0, -8, 0, 16, 0, 0, 432, 0, -16, 0, 32, 0, -568464, 0, 864, 0, -32, 0, 64, 0, 0, -1136928, 0, 1728, 0, -64, 0, 128, 0, 36058658688, 0, -2273856, 0, 3456, 0, -128, 0, 256, 0, 0, 72117317376, 0, -4547712, 0, 6912, 0, -256, 0, 512, 0
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Column k equals 2^k multiplied by column 0 (A111814) when ignoring zeros above the diagonal.
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FORMULA
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T(n, k) = 2^k*T(n-k, 0) = A111814(n-k) for n>=k>=0.
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EXAMPLE
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Matrix log of A078121, with factorial denominators, begins:
0;
1/1!, 0;
0/2!, 2/1!, 0;
-2/3!, 0/2!, 4/1!, 0;
0/4!, -4/3!, 0/2!, 8/1!, 0;
216/5!, 0/4!, -8/3!, 0/2!, 16/1!, 0;
0/6!, 432/5!, 0/4!, -16/3!, 0/2!, 32/1!, 0;
-568464/7!, 0/6!, 864/5!, 0/4!, -32/3!, 0/2!, 64/1!, 0; ...
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PROGRAM
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(PARI) {T(n, k, q=2)=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|j==1, B[i, j]=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. A078121, A111814 (column 0), A111810 (variant); log matrices: A110504 (q=-1), A111815 (q=3), A111818 (q=4), A111823 (q=5), A111828 (q=6), A111833 (q=7), A111838 (q=8).
Sequence in context: A046522 A112631 A096500 this_sequence A132952 A029187 A035385
Adjacent sequences: A111810 A111811 A111812 this_sequence A111814 A111815 A111816
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KEYWORD
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frac,sign,tabl
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AUTHOR
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Gottfried Helms (helms(AT)uni-kassel.de) and Paul D. Hanna (pauldhanna(AT)juno.com), Aug 22 2005
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