OFFSET
0,3
REFERENCES
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 5.2.7.
LINKS
T. D. Noe, Table of n, a(n) for n=0..100
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 584
H. Gupta, Enumeration of symmetric matrices, Duke Math. J., 35 (1968), vol 3, 653-659.
H. Gupta, Enumeration of symmetric matrices (annotated scanned copy)
Tomislav Došlic, Darko Veljan, Logarithmic behavior of some combinatorial sequences, Discrete Math. 308 (2008), no. 11, 2182--2212. MR2404544 (2009j:05019). - From N. J. A. Sloane, May 01 2012
FORMULA
E.g.f.: (1-x)^(-1/2)*exp(x^2/4 + x/(2*(1-x))).
a(n) ~ n^n*exp(sqrt(2*n)-n)/sqrt(2) * (1-5/(24*sqrt(2*n))). - Vaclav Kotesovec, Jul 29 2013
Recurrence: 2*a(n) = 2*(2*n-1)*a(n-1) - 2*(n-2)*(n-1)*a(n-2) - 2*(n-2)*(n-1)*a(n-3) + (n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Jul 29 2013
MATHEMATICA
max = 21; egf[x_] := (1-x)^(-1/2)*Exp[x^2/4 + x/(2*(1-x))]; CoefficientList[ Series[ egf[x], {x, 0, max}], x]*Range[0, max]! (* Jean-François Alcover, Nov 25 2011 *)
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
STATUS
approved