0,5

a(n) ~ n!*exp(-3/4)/sqrt(Pi*n).

a(n) is the number of ways of covering K_n with cycles of length >= 3. Also number of 'frames' on n lines: given n lines in general position (none parallel and no three concurrent), a frame is a subset of n of the e C(n,2) points of intersection such that no three points are on the same line. - Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu), Jul 06 2006

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 276 and 279.

Editorial note: Robinson's constant, Amer. Math. Monthly, 59 (1952), 296-297.

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.7.

Ph. Flajolet, Singular combinatorics, pp. 561-571, Proc. Internat. Congr. Math., Beijing 2002, Higher Education Press, Beijing, 2002, Vol III.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983, ex. 3.3.6b, 3.3.34.

R. Robinson, A new absolute geometric constant?, Amer. Math. Monthly, 58 (1951), 462-469.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.8. Also problems 5.23 and 5.15(a), case k=3.

H. S. Wilf, Generatingfunctionology, Academic Press, NY, 1990, p. 77, Eq. 3.9.1.

W. A. Whitworth, Choice and Chance, Bell, 1901, p. 269, ex. 160.

T. D. Noe, Table of n, a(n) for n=0..100

Ph. Flajolet, Singular combinatorics

Ph. Flajolet and A. Odlyzko, Singularity analysis of generating functions

H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 86, Eq. 3.9.1.

E.g.f.: exp(-x/2-x^2/4)/sqrt(1-x). a(n+1)=n(a(n)+a(n-2)(n-1)/2).

(PARI) a(n)=if(n<0, 0, n!*polcoeff(exp(-x/2-x^2/4+x*O(x^n))/sqrt(1-x+x*O(x^n)), n))

Cf. A000985, A000986, A002137. A diagonal of A059441.

Sequence in context: A113341 A125862 A077460 this_sequence A112320 A103366 A020530

Adjacent sequences: A001202 A001203 A001204 this_sequence A001206 A001207 A001208

nonn,easy,nice

njas