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A111838
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Matrix log of triangle A111835, which shifts columns left and up under matrix 8-th power; these terms are the result of multiplying each element in row n and column k by (n-k)!.
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8
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0, 1, 0, -6, 8, 0, 142, -48, 64, 0, 31800, 1136, -384, 512, 0, -159468264, 254400, 9088, -3072, 4096, 0, -2481298801008, -1275746112, 2035200, 72704, -24576, 32768, 0, 1414130111428687344, -19850390408064, -10205968896, 16281600, 581632, -196608, 262144, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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Column k equals 8^k multiplied by column 0 (A111839) when ignoring zeros above the diagonal.
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LINKS
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Table of n, a(n) for n=0..35.
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FORMULA
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T(n, k) = 8^k*T(n-k, 0) = A111839(n-k) for n>=k>=0.
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EXAMPLE
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Matrix log of A111835, with factorial denominators, begins:
0;
1/1!, 0;
-6/2!, 8/1!, 0;
142/3!, -48/2!, 64/1!, 0;
31800/4!, 1136/3!, -384/2!, 512/1!, 0;
-159468264/5!, 254400/4!, 9088/3!, -3072/2!, 4096/1!, 0; ...
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PROG
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(PARI) {T(n, k, q=8)=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. A111835, A111839 (column 0); log matrices: A110504 (q=-1), A111813 (q=2), A111815 (q=3), A111818 (q=4), A111823 (q=5), A111828 (q=6), A111833 (q=7).
Sequence in context: A072553 A089991 A083727 * A197479 A154513 A195716
Adjacent sequences: A111835 A111836 A111837 * A111839 A111840 A111841
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KEYWORD
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frac,sign,tabl
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AUTHOR
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Gottfried Helms and Paul D. Hanna, Aug 22 2005
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STATUS
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approved
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