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%I #22 Dec 30 2023 16:37:19
%S 1,1,1,1,2,4,2,1,1,2,8,17,24,24,17,8,2,1,1,2,9,32,95,203,373,515,584,
%T 515,373,203,95,32,9,2,1,1,2,9,36,157,549,1692,4374,9626,17874,28373,
%U 38486,44805,44805,38486,28373,17874,9626,4374,1692,549,157,36,9,2,1,1
%N Irregular triangle read by rows: T(n,k) = number of directed graphs-with-loops with n nodes and k arcs (n >= 0, 0 <= k <= n^2).
%C Equivalently, T(n,k) = number of relations on n-set with strength k (n >= 0, 0<=k<=n^2).
%D W. Oberschelp, Kombinatorische Anzahlbestimmungen in Relationen, Math. Ann., 174 (1967), 53-78.
%H W. Oberschelp, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002298732">Kombinatorische Anzahlbestimmungen in Relationen</a>, Math. Ann., 174 (1967), 53-78.
%e Triangle begins:
%e [1],
%e [1, 1],
%e [1, 2, 4, 2, 1],
%e [1, 2, 8, 17, 24, 24, 17, 8, 2, 1],
%e [1, 2, 9, 32, 95, 203, 373, 515, 584, 515, 373, 203, 95, 32, 9, 2, 1] (the last batch giving the numbers of directed graphs with loops on 4 nodes and from 0 to 16 arcs).
%t Needs["Combinatorica`"]; Join[{{1}, {1,1}}, CoefficientList[Table[CycleIndex[Join[PairGroup[SymmetricGroup[n], Ordered], Permutations[Range[n^2-n+1, n^2]], 2],s]/.Table[s[i]->1+x^i, {i,1,n^2-n}], {n,2,7}], x]]//Grid (* _Geoffrey Critzer_, Sep 29 2012 *)
%Y Cf. A000595.
%K nonn,tabf,nice
%O 0,5
%A _N. J. A. Sloane_
%E More terms from _Vladeta Jovovic_, Feb 07 2000
%E Edited by _N. J. A. Sloane_ Apr 16 2008 at the suggestion of Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 24 2008
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