A141771 Expansion of (1-sqrt(1-4*x))/(2*x) + 8*x^3/((sqrt(1-4*x))*(1+sqrt(1-4*x))^3).

1, 1, 2, 6, 19, 63, 216, 759, 2717, 9867, 36244, 134368, 501942, 1886966, 7131840, 27078705, 103221585, 394827315, 1514797020, 5827192140, 22469489130, 86825411010, 336145233840, 1303626531870, 5063559897474, 19695844095678, 76710709889576, 299125464317904

Offset

0,3

Links

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

Miklós Bóna, Permutations with one or two 132-subsequences, Discrete Math., 181 (1998) 267-274.

R. Brignall, S. Huczynska, V. Vatter, Decomposing simple permutations with enumerative consequences, Combinatorica, 28 (2008) 384-400.

Formula

a(n) = A000108(n) + A002054(n-2). - R. J. Mathar, Sep 18 2008

a(n) ~ 2^(2*n-3)/sqrt(Pi*n). - Vaclav Kotesovec, Jun 29 2013

Conjecture: (n+1) *(n^2+5*n-12) *(n^3-5*n^2+38*n-250)*a(n) -2 *(2*n-3) *(n^2+7*n-6) *(n^3-5*n^2+38*n-250) *a(n-1)=0. - R. J. Mathar, Apr 30 2016

Mathematica

a[n_] := Switch[n, 0, 1, 1, 1, _, CatalanNumber[n] + Binomial[2n-3, n-3]]; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Oct 06 2016, after R. J. Mathar *)

Prog

(PARI) x='x+O('x^40); Vec((1-sqrt(1-4*x))/(2*x) + 8*x^3/((sqrt(1-4*x))*(1+sqrt(1-4*x))^3)) \\ Michel Marcus, Oct 30 2015

Crossrefs

Sequence in context: A006724 A057409 A346157 * A001170 A001168 A193111

Adjacent sequences: A141768 A141769 A141770 * A141772 A141773 A141774

Keyword

nonn

Author

N. J. A. Sloane, Sep 18 2008

Status

approved