login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A113583 Number of permutations of length 2*n-1 with no local maxima in even positions. 4
1, 4, 56, 1632, 81664, 6241280, 676506624, 98709925888, 18655203885056, 4432984678858752, 1293646660855398400, 454816628946740707328, 189608469405709753122816, 92483656403812275277791232, 52178449263441077156062429184, 33716638014695384983287984291840, 24738782851403087736929931445141504 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is also the number of binary trees with n nodes such that each node and each edge is labeled uniquely from {1,...,2n-1} and the label of each node is less than the labels below it. - Brad R. Jones, Aug 13 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

C. Coscia, J. DeWitt, F. Yang, Y. Zhang, Online and Random Domination of Graphs, arXiv preprint arXiv:1509.08876 [math.CO], 2015-2017.

B. R. Jones, On tree hook length formulas, Feynman rules and B-series, Master's thesis, Simon Fraser University, 2014.

D. E. Knuth, Whirlpool Permutations, May 05 2020

M. La Croix, A combinatorial proof of a result of Gessel and Greene, Discr. Math., 306 (2006), 2251-2256.

FORMULA

E.g.f. (odd powers only): Sum_{n>=1} a(n) * x^(2*n-1)/(2*n-1)! = tanh(x)/(1-x*tanh(x)).

a(n) = (2*n-1)!*Sum(m=1..2*n, Sum(k=0..2*n-2*m, binomial(k+m-1,m-1)*(k+m)!*(-1)^k*2^(2*n-2*m-k)*Stirling2(2*n-m,k+m))/(2*n-m)!). - Vladimir Kruchinin, Jun 14 2011

a(n) ~ 2*(2*n-1)! / r^(2*n+2), where r = 1.1996786402577... is the root of the equation (r-1)*exp(2*r) = r+1. - Vaclav Kotesovec, Dec 10 2013

MATHEMATICA

Table[n!*SeriesCoefficient[Tanh[x]/(1-x*Tanh[x]), {x, 0, n}], {n, 1, 41, 2}] (* Vaclav Kotesovec, Dec 10 2013 *)

PROG

(Maxima)

a(n):=(2*n-1)!*sum(sum(binomial(k+m-1, m-1)*(k+m)!*(-1)^k*2^(2*n-2*m-k)*stirling2(2*n-m, k+m), k, 0, 2*n-2*m)/(2*n-m)!, m, 1, 2*n); /* Vladimir Kruchinin, Jun 14 2011 */

CROSSREFS

Cf. A122647.

Sequence in context: A277038 A009536 A009558 * A174489 A009563 A261747

Adjacent sequences:  A113580 A113581 A113582 * A113584 A113585 A113586

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 21 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 17 16:58 EST 2022. Contains 350402 sequences. (Running on oeis4.)