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A174195 Number of permutations of 1..n that almost avoid 231. 2
1, 1, 2, 6, 24, 111, 531, 2519, 11726, 53547, 240448, 1064608, 4658952, 20192022, 86807865, 370665585, 1573606410, 6647552115, 27962334180, 117185243340, 489508952160, 2038937744610, 8471179017990, 35115582053214, 145269385076124, 599866065025406, 2472955722033776, 10179494703130704, 41844811399520752, 171796056971896588 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

R. Brignall et al., Almost avoiding permutations, Discrete Math., 309 (2009), 6626-6631.

FORMULA

G.f.: (1-5*x-6*x^2 + 45*x^3-24*x^4-(1 + x-4*x^2 + x^3)*(1-4*x)^(3/2))/(-2*x^2*(1-4*x)^(3/2)).

a(n) ~ 2^(2*n-2)*sqrt(n)/sqrt(Pi). - Vaclav Kotesovec, Aug 23 2014

Conjecture: 2*(n+2)*(2013*n^2-10435*n+41550)*a(n) +(4026*n^3 -128025*n^2 +34955*n+59010)*a(n-1) -2 *(2*n-5)*(20130*n^2 -110855*n +93819) *a(n-2)=0. - R. J. Mathar, Jun 14 2016

MATHEMATICA

CoefficientList[Series[(1 - 5*x - 6*x^2 + 45*x^3 - 24*x^4 - (1 + x - 4*x^2 + x^3)*(1 - 4*x)^(3/2))/(-2*x^2*(1 - 4*x)^(3/2)), {x, 0, 50}], x] (* G. C. Greubel, Mar 22 2017 *)

PROG

(PARI) x='x+O('x^50); Vec((1 - 5*x - 6*x^2 + 45*x^3 - 24*x^4 - (1 + x - 4*x^2 + x^3)*(1 - 4*x)^(3/2))/(-2*x^2*(1 - 4*x)^(3/2))) \\ G. C. Greubel, Mar 22 2017

CROSSREFS

Cf. A174193.

Sequence in context: A138020 A046646 A342284 * A274378 A177521 A152322

Adjacent sequences:  A174192 A174193 A174194 * A174196 A174197 A174198

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 26 2010

STATUS

approved

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Last modified January 22 02:46 EST 2022. Contains 350481 sequences. (Running on oeis4.)