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Search: id:A111828
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| A111828 |
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Matrix log of triangle A111825, which shifts columns left and up under matrix 6-th power; 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, -4, 6, 0, 42, -24, 36, 0, 7296, 252, -144, 216, 0, -7931976, 43776, 1512, -864, 1296, 0, -45557382240, -47591856, 262656, 9072, -5184, 7776, 0, 3064554175021200, -273344293440, -285551136, 1575936, 54432, -31104, 46656, 0, 801993619807364206080
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Column k equals 6^k multiplied by column 0 (A111829) when ignoring zeros above the diagonal.
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FORMULA
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T(n, k) = 6^k*T(n-k, 0) = A111829(n-k) for n>=k>=0.
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EXAMPLE
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Matrix log of A111825, with factorial denominators, begins:
0;
1/1!, 0;
-4/2!, 6/1!, 0;
42/3!, -24/2!, 36/1!, 0;
7296/4!, 252/3!, -144/2!, 216/1!, 0;
-7931976/5!, 43776/4!, 1512/3!, -864/2!, 1296/1!, 0; ...
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PROGRAM
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(PARI) {T(n, k, q=6)=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. A111825, A111829 (column 0); log matrices: A110504 (q=-1), A111813 (q=2), A111815 (q=3), A111818 (q=4), A111823 (q=5), A111833 (q=7), A111838 (q=8).
Sequence in context: A011442 A135183 A021221 this_sequence A013249 A013253 A013246
Adjacent sequences: A111825 A111826 A111827 this_sequence A111829 A111830 A111831
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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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