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A228534
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Triangular array read by rows: T(n,k) is the number of functional digraphs on {1,2,...,n} such that every element is mapped to a recurrent element and there are exactly k cycles, n>=1, 1<=k<=n.
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1
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1, 3, 1, 11, 9, 1, 58, 71, 18, 1, 409, 620, 245, 30, 1, 3606, 6274, 3255, 625, 45, 1, 38149, 73339, 45724, 11795, 1330, 63, 1, 470856, 977780, 697004, 221529, 33880, 2506, 84, 1, 6641793, 14678712, 11602394, 4309956, 823179, 82908, 4326, 108, 1
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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.: 1/(1 - x*exp(x))^y.
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EXAMPLE
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1;
3, 1;
11, 9, 1;
58, 71, 18, 1;
409, 620, 245, 30, 1;
3606, 6274, 3255, 625, 45, 1;
38149, 73339, 45724, 11795, 1330, 63, 1;
470856, 977780, 697004, 221529, 33880, 2506, 84, 1;
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MAPLE
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# The function BellMatrix is defined in A264428.
# Adds (1, 0, 0, 0, ..) as column 0.
g := n -> add(m^(n-m)*m!*binomial(n+1, m), m=1..n+1);
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MATHEMATICA
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nn = 8; a = x Exp[x];
Map[Select[#, # > 0 &] &,
Drop[Range[0, nn]! CoefficientList[
Series[1/(1 - a)^y, {x, 0, nn}], {x, y}], 1]] // Grid
(* Second program: *)
BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
B = BellMatrix[Function[n, (n+1)! Sum[m^(n-m)/(n-m+1)!, {m, 1, n+1}]], rows = 12];
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PROG
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# Adds a column 1, 0, 0, 0, ... at the left side of the triangle.
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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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