0,2

For n>1, a(n)=(1/2)*A001813(n+1). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2007

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

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

L. W. Beineke and R. E. Pippert, Enumerating labeled k-dimensional trees and ball dissections, pp. 12-26 of Proceedings of Second Chapel Hill Conference on Combinatorial Mathematics and Its Applications, University of North Carolina, Chapel Hill, 1970. Reprinted in Math. Annalen, 191 (1971), 87-98.

L. C. Larson, The number of essentially different nonattacking rook arrangements, J. Recreat. Math., 7 (No. 3, 1974), circa pages 180-181.

DAN LEVY AND LIOR PACHTER, THE NEIGHBOR-NET ALGORITHM, arXiv:math/0702515v2,

Lee A. Newberg, The Number of Clone Orderings, Discrete Applied Mathematics, Vol. 69 (1996), pp. 233-245.

R. W. Robinson, Counting arrangements of bishops, pp. 198-214 of Combinatorial Mathematics IV (Adelaide 1975), Lect. Notes Math., 560 (1976).

H. E. Salzer, Coefficients for expressing the first thirty powers in terms of the Hermite polynomials, Math. Comp., 3 (1948), 167-169.

H. E. Salzer, Orthogonal polynomials arising in the evaluation of inverse Laplace transforms, Math. Comp. 9 (1955), 164-177.

N. J. A. Sloane, Table of n, a(n) for n = 0..100

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 139

Index entries for sequences related to factorial numbers

E.g.f.: (1+2*x-sqrt(1-4*x))/4.

E.g.f. for a(n-1), n >= 0, with a(-1) := 0 is (-1+1/(1-4*x)^(1/2))/2. 2*a(n)=(4*n+2)(!^4) := product(4*j+2, j=0..n), (one half of 4-factorial numbers) [ wolfdieter.lang(AT)physik.uni-karlsruhe.de ]

a(n)=C(n+1)*(n+2)!/2; - Paul Barry (pbarry(AT)wit.ie), Feb 16 2005

For asymptotics see the Robinson paper.

For Maple program see A000903.

with(finance):seq(mul(cashflows([n, k, 1], 0), k=0..n), n=0..22); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]

a := n -> pochhammer(n, n); (for n>0) [From Peter Luschny (peter(AT)luschny.de), Feb 14 2009]

Table[(2n + 1)!/n!, {n, 0, 30}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 5, 5!, 4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 08 2008]

Cf. A001761-A001763, A007696.

A100622 is the "Number of topologically distinct solutions to the clone ordering problem for n clones" without the restriction that they be in a single contig.

Sequence in context: A120973 A101470 A066151 this_sequence A099708 A010040 A138379

Adjacent sequences: A000404 A000405 A000406 this_sequence A000408 A000409 A000410

nonn,easy,nice

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