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Search: id:A101897
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| A101897 |
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Triangle T, read by rows, such that column k equals column 0 of T^(k+1), where column 0 of T allows the n-th row sums to be zero for n>0, and where T^k is the k-th power of T as a lower triangular matrix. |
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+0
5
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| 1, -1, 1, 1, -2, 1, -2, 4, -3, 1, 5, -11, 9, -4, 1, -17, 38, -33, 16, -5, 1, 71, -162, 145, -74, 25, -6, 1, -357, 824, -753, 396, -140, 36, -7, 1, 2101, -4892, 4535, -2434, 885, -237, 49, -8, 1, -14203, 33286, -31185, 16982, -6295, 1730, -371, 64, -9, 1, 108609, -255824, 241621, -133012, 50001, -13992, 3073, -548, 81
(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 0 forms A101900. Absolute row sums form A101901.
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FORMULA
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T(n, k) = Sum_{j=0..n-k} T(n-k, j)*T(j+k-1, k-1) for n>=k>0 with T(0, 0)=1 and T(n, 0) = -Sum_{j=1, n} T(n, j) for n>0.
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EXAMPLE
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Rows begin:
[1],
[ -1,1],
[1,-2,1],
[ -2,4,-3,1],
[5,-11,9,-4,1],
[ -17,38,-33,16,-5,1],
[71,-162,145,-74,25,-6,1],
[ -357,824,-753,396,-140,36,-7,1],
[2101,-4892,4535,-2434,885,-237,49,-8,1],
[ -14203,33286,-31185,16982,-6295,1730,-371,64,-9,1],...
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PROGRAM
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(PARI) {T(n, k)=if(k>n|n<0|k<0, 0, if(k==n, 1, if(k==0, -sum(j=1, n, T(n, j)), sum(j=0, n-k, T(n-k, j)*T(j+k-1, k-1)); )); )}
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CROSSREFS
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Cf. A091351, A101900, A101901, A101898, A101899.
Sequence in context: A137406 A120855 A091173 this_sequence A078142 A133422 A099312
Adjacent sequences: A101894 A101895 A101896 this_sequence A101898 A101899 A101900
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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), Dec 20 2004
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