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Search: id:A111548
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| 1, -1, 1, -3, -2, 1, -15, -3, -3, 1, -99, -15, -3, -4, 1, -783, -99, -15, -3, -5, 1, -7083, -783, -99, -15, -3, -6, 1, -71415, -7083, -783, -99, -15, -3, -7, 1, -789939, -71415, -7083, -783, -99, -15, -3, -8, 1, -9485343, -789939, -71415, -7083, -783, -99, -15, -3, -9, 1, -122721723, -9485343, -789939, -71415
(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 all equal after the initial terms, and are derived from the logarithm of a factorial series (cf. A111546).
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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) = -A111546(k) for k>=1.
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EXAMPLE
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Triangle begins:
1;
-1,1;
-3,-2,1;
-15,-3,-3,1;
-99,-15,-3,-4,1;
-783,-99,-15,-3,-5,1;
-7083,-783,-99,-15,-3,-6,1;
-71415,-7083,-783,-99,-15,-3,-7,1;
-789939,-71415,-7083,-783,-99,-15,-3,-8,1; ...
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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-k, (i+2)!/2!*x^i)), n-k-1))))}
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CROSSREFS
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Cf. A111544, A111546, A111540.
Sequence in context: A129652 A127126 A112911 this_sequence A140709 A109282 A135902
Adjacent sequences: A111545 A111546 A111547 this_sequence A111549 A111550 A111551
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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 07 2005
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