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A098493
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Triangle T(n,k) read by rows: difference between A098489 and A098490 at triangular rows.
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5
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1, 0, -1, -1, -1, 1, -1, 1, 2, -1, 0, 3, 0, -3, 1, 1, 2, -5, -2, 4, -1, 1, -2, -7, 6, 5, -5, 1, 0, -5, 0, 15, -5, -9, 6, -1, -1, -3, 12, 9, -25, 1, 14, -7, 1, -1, 3, 15, -18, -29, 35, 7, -20, 8, -1, 0, 7, 0, -42, 14, 63, -42, -20, 27, -9, 1, 1, 4, -22, -24, 85, 14, -112, 42
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| Also, coefficients of polynomials that have values in A098495 and A094954.
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REFERENCES
| A. Fink, R. K. Guy and M. Krusemeyer, Partitions with parts occurring at most thrice, in preparation.
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FORMULA
| T(n, k) = A098489[n(n+1)/2, k] - A098490[n(n+1)/2, k].
Recurrence: T(n, k) = T(n-1, k)-T(n-1, k-1)-T(n-2, k); T(n, k)=0 for n<0, k>n, k<0; T(n, n)=(-1)^n; T(n, n-1)=(-1)^n*(1-n).
G.f.: (1-x)/(1+(y-1)*x+x^2). [From Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 14 2009]
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EXAMPLE
| {1} {0,-1} {-1,-1,1} {-1,1,2,-1} {0,3,0,-3,1}...
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PROG
| (PARI) T(n, k)=if(k>n||k<0||n<0, 0, if(k>=n-1, (-1)^n*if(k==n, 1, -k), if(n==1, 0, if(k==0, T(n-1, 0)-T(n-2, 0), T(n-1, k)-T(n-2, k)-T(n-1, k-1)))))
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CROSSREFS
| Columns include A010892, -A076118. Diagonals include A033999, A038608, (-1)^n*A000096. Row sums are in A057077.
Cf. A098494 (diagonal polynomials).
Sequence in context: A178780 A058558 A123973 * A058560 A131047 A143714
Adjacent sequences: A098490 A098491 A098492 * A098494 A098495 A098496
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KEYWORD
| sign,tabl
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AUTHOR
| Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 12 2004
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