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A294735
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Triangle read by rows: T(n,k) (3 <= k < n) gives number of solutions to certain 1-loop scattering equations refined by MHV degree.
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0
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2, 6, 6, 14, 44, 14, 30, 210, 210, 30, 62, 832, 1812, 832, 62, 126, 2982, 12012, 12012, 2982, 126, 254, 10068, 68322, 124952, 68322, 10068, 254, 510, 32730, 352350, 1065930, 1065930, 352350, 32730, 510, 1022, 103784, 1700456, 7972568, 13103540, 7972568, 1700456, 103784, 1022
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OFFSET
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4,1
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COMMENTS
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See Appendix E of Farrow and Lipstein.
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LINKS
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FORMULA
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T(n,k) = euler(n-1,k-1) - euler(n-2,k-1) - euler(n-2,k-2), where euler = A008292.
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EXAMPLE
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Triangle begins
2
6, 6
14, 44, 14
30, 210, 210, 30
62, 832, 1812, 832, 62
126, 2982, 12012, 12012, 2982, 126
254, 10068, 68322, 124952, 68322, 10068, 254
510, 32730, 352350, 1065930, 1065930, 352350, 32730, 510
1022, 103784, 1700456, 7972568, 13103540, 7972568, 1700456, 103784, 1022
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MATHEMATICA
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e[n_, k_] := Sum[(-1)^j (k - j)^n Binomial[n + 1, j], {j, 0, k}];
T[n_, k_] := e[n - 1, k - 1] - e[n - 2, k - 1] - e[n - 2, k - 2];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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