0,2

Number of tableaux on 2n elements. - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 09 2002

a(n) = number of ways to connect 2n points labeled 1,2,...,2n in a line with 0 or more arcs such that at most one arc leaves each point. For example, with arcs separated by dashes, a(2)=10 counts {} (no arcs), 12, 13, 14, 23, 24, 34, 12-34, 13-24, 14-23. - David Callan (callan(AT)stat.wisc.edu), Sep 18 2007

S. Chowla, The asymptotic behavior of solutions of difference equations, in Proceedings of the International Congress of Mathematicians (Cambridge, MA, 1950), Vol. I, 377, Amer. Math. Soc., Providence, RI, 1952.

a(n)=sum(k=0, n, C(2n, 2*k)*(2k-1)!!) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 01 2003

n!*2^n*LaguerreL(n, -1/2, -1/2). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 10 2003

E.g.f.: cosh(x)exp(x^2/2) (with interpolated zeros) - Paul Barry (pbarry(AT)wit.ie), May 26 2003

NumberOfTableaux[2n]

(PARI) a(n)=sum(k=0, n, binomial(2*n, 2*k)*prod(i=1, k, 2*i-1))

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

Cf. A066224.

Sequence in context: A094071 A136222 A124426 this_sequence A088500 A095789 A134980

Adjacent sequences: A066220 A066221 A066222 this_sequence A066224 A066225 A066226

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com), Dec 19 2001

More terms from Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 09 2002