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Search: id:A111540
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| 1, -1, 1, -2, -2, 1, -8, -2, -3, 1, -44, -8, -2, -4, 1, -296, -44, -8, -2, -5, 1, -2312, -296, -44, -8, -2, -6, 1, -20384, -2312, -296, -44, -8, -2, -7, 1, -199376, -20384, -2312, -296, -44, -8, -2, -8, 1, -2138336, -199376, -20384, -2312, -296, -44, -8, -2, -9, 1, -24936416, -2138336, -199376, -20384, -2312, -296
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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The column sequences are derived from the logarithm of a factorial series (cf. A111537).
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FORMULA
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T(n, n)=1 and T(n+1, n)=n+1, else T(n+k+1, k) = -A111537(k) for k>=1.
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EXAMPLE
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Triangle begins:
1;
-1,1;
-2,-2,1;
-8,-2,-3,1;
-44,-8,-2,-4,1;
-296,-44,-8,-2,-5,1;
-2312,-296,-44,-8,-2,-6,1;
-20384,-2312,-296,-44,-8,-2,-7,1;
-199376,-20384,-2312,-296,-44,-8,-2,-8,1; ...
After initial terms, all columns are equal to -A111537.
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PROGRAM
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(PARI) {T(n, k)=if(n<k|k<0, 0, if(n==k, 1, if(n==k+1, -n, -(n-k-1)*polcoeff(log(sum(i=0, n, (i+1)!/1!*x^i)), n-k-1))))}
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CROSSREFS
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Cf. A111536, A111537.
Adjacent sequences: A111537 A111538 A111539 this_sequence A111541 A111542 A111543
Sequence in context: A021455 A136502 A100632 this_sequence A096440 A121350 A135080
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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), Aug 06 2005
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