A272429 Asymptotic mean (normalized by n) of the second largest connected component in a random mapping on n symbols.

1, 7, 0, 9, 0, 9, 6, 1, 9, 8, 5, 9, 6, 6, 2, 3, 9, 2, 1, 4, 4, 6, 0, 7, 2, 8, 4, 1, 3, 3, 1, 1, 7, 3, 8, 7, 0, 4, 7, 1, 9, 0, 7, 2, 9, 6, 2, 6, 2, 8, 8, 3, 2, 3, 5, 5, 8, 5, 3, 8, 8, 1, 0, 0, 6, 3, 9, 8, 3, 6, 9, 5, 3, 0, 1, 5, 3, 7, 3, 9, 8, 9, 6, 4, 8, 2, 6, 6, 5, 3, 7, 5, 5, 3, 5

Offset: 0

Author

Jean-François Alcover, Apr 29 2016

Keywords

• nonn
• cons

Examples

			0.17090961985966239214460728413311738704719072962628832355853881...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.4.2 Random mapping statistics, p. 290.

Links

• Xavier Gourdon, Combinatoire, Algorithmique et Géométrie des Polynomes Ecole Polytechnique, Paris 1996, page 152 (in French)
• Eric Weisstein's MathWorld, Flajolet-Odlyzko Constant

Crossrefs

Cf. A084945, A143297, A261873.

Programs

Mathematica

digits = 95; Ei = ExpIntegralEi; 2*NIntegrate[1 - E^(Ei[-x]/2)*(1 - Ei[-x]/2), {x, 0, 200}, WorkingPrecision -> digits + 5] // RealDigits[#, 10, digits]& // First

Formula

2*integral_{0..infinity} 1 - e^(Ei(-x)/2)*(1 - Ei(-x)/2) dx, where Ei is the exponential integral.