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A247232
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Triangular array read by rows: T(n,k) is the number of pre-orders on an n-set with exactly k connected components in its digraph representation, n>=1, 1<=k<=n.
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1
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1, 3, 1, 19, 9, 1, 233, 103, 18, 1, 4851, 1735, 325, 30, 1, 158175, 43201, 7320, 785, 45, 1, 7724333, 1567783, 218491, 22960, 1610, 63, 1, 550898367, 82142943, 8856974, 818461, 59570, 2954, 84, 1, 56536880923, 6187176225, 496368181, 37205658, 2518131, 135198, 4998, 108, 1
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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E.g.f.: A(exp(x)-1)^y where A(x) is the e.g.f. for A001035.
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EXAMPLE
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1;
3, 1;
19, 9, 1;
233, 103, 18, 1;
4851, 1735, 325, 30, 1;
158175, 43201, 7320, 785, 45, 1;
7724333, 1567783, 218491, 22960, 1610, 63, 1;
550898367, 82142943, 8856974, 818461, 59570, 2954, 84, 1;
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MATHEMATICA
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A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {_, _}][[All, 2]];
A[x_] = Sum[A001035[[n + 1]] x^n/n!, {n, 0, lg - 1}];
Rest[CoefficientList[#, y]]& /@ (CoefficientList[A[Exp[x] - 1]^y + O[x]^lg, x]*Range[0, lg - 1]!) // Flatten (* Jean-François Alcover, Jan 01 2020 *)
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PROG
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(Sage) # uses[bell_matrix from A264428]
# Adds a column 1, 0, 0, 0, ... at the left side of the triangle.
topo = oeis('A001929') # Fetch the data via Internet.
A001929List = topo.first_terms()
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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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