A175716 The total number of elements(ordered pairs) in all equivalence relations on {1,2,...,n}.

0, 1, 6, 27, 120, 560, 2778, 14665, 82232, 488403, 3062980, 20221520, 140134404, 1016698813, 7703878042, 60833235795, 499592325152, 4259301450652, 37634032670886, 344092369602461, 3250925202629100

Offset: 0

Author

Geoffrey Critzer, Dec 04 2010

Keywords

• nonn
• changed

Examples

			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.
		

Crossrefs

Cf. A124427, A000595.

Programs

Mathematica

f[list_] := Length[list]^2; Table[Total[Map[f, Level[SetParttions[n], {2}]]], {n, 0, 12}] (* or *)
Range[0,20]! CoefficientList[Series[(x + x^2)Exp[x] * Exp[Exp[x] - 1], {x, 0, 20}], x]

Formula

a(n) = n*A124427(n). - Joerg Arndt, Dec 04 2010

E.g.f.: (x+x^2) * exp(x) * exp(exp(x)-1).