This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A175716 #19 Sep 02 2025 21:54:47
%S A175716 0,1,6,27,120,560,2778,14665,82232,488403,3062980,20221520,140134404,
%T A175716 1016698813,7703878042,60833235795,499592325152,4259301450652,
%U A175716 37634032670886,344092369602461,3250925202629100
%N A175716 The total number of elements(ordered pairs) in all equivalence relations on {1,2,...,n}.
%F A175716 a(n) = n*A124427(n). - _Joerg Arndt_, Dec 04 2010
%F A175716 E.g.f.: (x+x^2) * exp(x) * exp(exp(x)-1).
%e A175716 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 A175716 f[list_] := Length[list]^2; Table[Total[Map[f, Level[SetParttions[n], {2}]]], {n, 0, 12}] (* or *)
%t A175716 Range[0,20]! CoefficientList[Series[(x + x^2)Exp[x] * Exp[Exp[x] - 1], {x, 0, 20}], x]
%Y A175716 Cf. A124427, A000595.
%K A175716 nonn,changed
%O A175716 0,3
%A A175716 _Geoffrey Critzer_, Dec 04 2010