A225723 Triangular array read by rows: T(n,k) is the number of size k components in the digraph representation of all functions f:{1,2,...,n}->{1,2,...,n}; n>=1, 1<=k<=n.
1, 2, 3, 12, 9, 17, 108, 72, 68, 142, 1280, 810, 680, 710, 1569, 18750, 11520, 9180, 8520, 9414, 21576, 326592, 196875, 152320, 134190, 131796, 151032, 355081, 6588344, 3919104, 2975000, 2544640, 2372328, 2416512, 2840648, 6805296
Offset: 1
Examples
Triangle T(n,k) begins:
1;
2, 3;
12, 9, 17;
108, 72, 68, 142;
1280, 810, 680, 710, 1569;
18750, 11520, 9180, 8520, 9414, 21576;
326592, 196875, 152320, 134190, 131796, 151032, 355081;
...
Links
- Alois P. Heinz, Rows n = 1..100, flattened
Crossrefs
Cf. A225213.
Programs
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Maple
b:= n-> n!*add(n^(n-k-1)/(n-k)!, k=1..n): T:= (n, k)-> binomial(n,k)*b(k)*(n-k)^(n-k): seq(seq(T(n, k), k=1..n), n=1..10); # Alois P. Heinz, May 13 2013
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Mathematica
nn = 8; tx = Sum[n^(n - 1) x^n/n!, {n, 1, nn}]; txy = Sum[n^(n - 1) (x y)^n/n!, {n, 1, nn}]; Map[Select[#, # > 0 &] &, Drop[Range[0, nn]! CoefficientList[ Series[Log[1/(1 - txy)]/(1 - tx), {x, 0, nn}], {x, y}], 1]] // Grid
Formula
E.g.f.: log(1/(1 - A(x*y)))/(1 - A(x)) where A(x) is the e.g.f. for A000169.
Comments