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.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

Z. Tan and S. Gao, Enumeration of (0,1)-Symmetric Matrices, submitted [From Shanzhen Gao (sgao2(AT)fau.edu), Jun 05 2009]

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).

$\frac{1}{4^{n}}\sum_{\beta =0}^{\lfloor \frac{n}{2}\rfloor }\sum_{\gamma =0}^{n-2\beta }\frac{(-1)^{\beta +\gamma }2^{2\beta +\gamma }n!(2n-4\beta -2\gamma )!}{\beta !\gamma !((n-2\beta -\gamma )!)^{2}}$ [From Shanzhen Gao (sgao2(AT)fau.edu), Jun 05 2009]

(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

N. J. A. Sloane (njas(AT)research.att.com).