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A350571
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Triangular array read by rows. T(n,k) is the number of unlabeled partial functions on [n] with exactly k undefined points, n>=0, 0<=k<=n.
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0
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1, 1, 1, 3, 2, 1, 7, 6, 2, 1, 19, 16, 7, 2, 1, 47, 45, 19, 7, 2, 1, 130, 121, 57, 20, 7, 2, 1, 343, 338, 158, 60, 20, 7, 2, 1, 951, 929, 457, 170, 61, 20, 7, 2, 1, 2615, 2598, 1286, 498, 173, 61, 20, 7, 2, 1, 7318, 7261, 3678, 1421, 510, 174, 61, 20, 7, 2, 1
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OFFSET
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0,4
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COMMENTS
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It appears that the columns converge to A116950.
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REFERENCES
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O. Ganyushkin and V. Mazorchuk, Classical Finite Transformation Semigroups, Springer, 2009.
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LINKS
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FORMULA
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G.f.: Product_{i>=1} 1/(1-y*x^i)^A000081(i)*Product_{i>=1} 1/(1-x^i)^A002861(i).
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EXAMPLE
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Triangle T(n,k) begins:
1;
1, 1;
3, 2, 1;
7, 6, 2, 1;
19, 16, 7, 2, 1;
47, 45, 19, 7, 2, 1;
130, 121, 57, 20, 7, 2, 1;
343, 338, 158, 60, 20, 7, 2, 1;
951, 929, 457, 170, 61, 20, 7, 2, 1;
...
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MATHEMATICA
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nn = 10; A002861 = Cases[Import["https://oeis.org/A002861/b002861.txt",
"Table"], {_, _}][[;; nn, 2]];
"Table"], {_, _}][[;; nn + 1, 2]], 1];
Map[Select[#, # > 0 &] &, CoefficientList[Series[ Product[1/(1 - y x^i)^A000081[[i]], {i, 1, nn}] Product[1/(1 - x^i)^A002861[[i]], {i, 1, nn}], {x, 0, nn}], {x, y}]] // Grid
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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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