0,3

Or, number of labeled 2-regular pseudodigraphs (multiple arcs and loops allowed) of order n.

H. Anand, V. C. Dumir and H. Gupta, A combinatorial distribution problem, Duke Math. J., 33 (1996), 757-769.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 125, #25, a_n.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, John Wiley and Sons, N.Y., 1983, section 3.5.10.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1982.

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Cor. 5.5.11 (a).

M. L. Stein and P. R. Stein, Enumeration of Stochastic Matrices with Integer Elements. Report LA-4434, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Jun 1970.

C. B. Tompkins, Methods of successive restrictions in computational problems involving discrete variables. 1963, Proc. Sympos. Appl. Math., Vol. XV pp. 95-106; Amer. Math. Soc., Providence, R.I.

Zhonghua,Tan and Shanzhen Gao, Counting (0,1,2)-Matrices, submitted.

R. W. Robinson, Table of n, a(n) for n = 0..48

Ira Gessel, Enumerative applications of symmetric functions

Index entries for sequences related to magic squares

Sum_{n >= 0} a(n) x^n / n!^2 = 1/(1-x)^(1/2)*exp(1/2*x).

a(n) = n^2*a(n-1) - (1/2)*n*(n-1)^2*a(n-2).

a(n) is asymptotic to c/sqrt(n)*(n!)^2 where c=0.93019... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 25 2004

Sum[i=0..n, 2^(i-2n) * C(n, i)^2 * (2n-2i)! * i! ].

a(n)=2^{-n}\sum_{i=0}^{n}\frac{(n!)^{2}(2i)!}{(i!)^{2}((n-i)!2^{i})} - Shanzhen Gao (sgao2(AT)fau.edu), Nov 05 2007

Cf. A001499, A005650, A123544.

Sequence in context: A066206 A130032 A126461 this_sequence A055555 A005329 A134528

Adjacent sequences: A000678 A000679 A000680 this_sequence A000682 A000683 A000684

nonn,nice,easy

njas, Simon Plouffe (plouffe(AT)math.uqam.ca)

More terms from David W. Wilson (davidwwilson(AT)comcast.net)