login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A071075 Number of permutations that avoid the generalized pattern 132-4. 4
1, 1, 2, 6, 23, 107, 585, 3671, 25986, 204738, 1776327, 16824237, 172701135, 1909624371, 22626612450, 285982186662, 3840440707485, 54603776221965, 819424594880559, 12942757989763101, 214626518776190178, 3728112755679416898, 67692934780306842501, 1282399636333412178531, 25303124674163685176793 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..460

A. M. Baxter, Algorithms for Permutation Statistics, Ph. D. Dissertation, Rutgers University, May 2011.

Andrew M. Baxter and Lara K. Pudwell, Enumeration schemes for dashed patterns, arXiv:1108.2642 [math.CO], 2011.

S. Kitaev, Partially Ordered Generalized Patterns, Discrete Math. 298 (2005), no. 1-3, 212-229.

FORMULA

E.g.f.: exp(int(A(y), y=0..x)), where A(y) = 1/(1-int(exp(-t^2/2), t=0..y)).

a(n) ~ c * d^n * n! / n^f, where d = 1/(sqrt(2)*InverseErf(sqrt(2/Pi))) = 0.7839769312035474991242486548698125357473282..., f = 1.2558142944089303287268746534354522944538722816671534535062816..., c = 0.2242410644782853722452053227678681810005068... . - Vaclav Kotesovec, Aug 23 2014

MAPLE

A(y) := 1/(1-int(exp(-t^2/2), t=0..y)); B(x) := exp(int(A(y), y=0..x)); series(B(x), x=0, 30);

MATHEMATICA

CoefficientList[Series[E^(Integrate[1/(1-Integrate[E^(-t^2/2), {t, 0, y}]), {y, 0, x}]), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Aug 23 2014 *)

PROG

(PARI)

N=66; x='x+O('x^N);

A=1/(1-intformal(exp(-x^2/2)));

egf=exp(intformal(A));

Vec(serlaplace(egf))

\\ Joerg Arndt, Aug 28 2014

CROSSREFS

Cf. A071088, A071076, A071077.

Sequence in context: A200405 A200403 A113226 * A007555 A101053 A155857

Adjacent sequences:  A071072 A071073 A071074 * A071076 A071077 A071078

KEYWORD

nonn

AUTHOR

Sergey Kitaev (kitaev(AT)math.chalmers.se), May 26 2002

EXTENSIONS

Link and a(11)-a(20) from Andrew Baxter, May 17 2011

Typo in first formula corrected by Vaclav Kotesovec, Aug 23 2014

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 February 20 00:28 EST 2019. Contains 320329 sequences. (Running on oeis4.)