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%I #13 Mar 30 2012 17:23:10
%S 0,1,6,27,120,560,2778,14665,82232,488403,3062980,20221520,140134404,
%T 1016698813,7703878042,60833235795,499592325152,4259301450652,
%U 37634032670886,344092369602461,3250925202629100
%N The total number of elements(ordered pairs) in all equivalence relations on {1,2,...,n}
%F a(n) = n*A124427(n). - Joerg Arndt, Dec 04 2010.
%F E.g.f.: (x+x^2) * exp(x) * exp(exp(x)-1).
%e a(2)= 6 because the equivalence relations on {1,2}: {(1,1), (2,2)}, {(1,1), (2,2), (1,2), (2,1)} contain 6 ordered pairs.
%t f[list_] := Length[list]^2; Table[Total[Map[f, Level[SetParttions[n], {2}]]], {n, 0, 12}] (* or *)
%t Range[0,20]! CoefficientList[Series[(x + x^2)Exp[x] * Exp[Exp[x] - 1], {x, 0, 20}], x]
%Y Cf. A124427, A000595.
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Dec 04 2010