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A065087

a(n) = A000166(n)*binomial(n+1,2).

0, 0, 3, 12, 90, 660, 5565, 51912, 533988, 6007320, 73422855, 969181620, 13744757598, 208462156812, 3367465610145, 57727981888080, 1046800738237320, 20020064118788592, 402756584036805963, 8502638996332570140, 187953072550509445410, 4341715975916768188740

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OFFSET

0,3

COMMENTS

a(n) is also the number of permutations of [2n-1] having n-1 isolated fixed points (i.e., adjacent entries are not fixed points). Example: a(2) = 3 because we have 132, 213, and 321. - Emeric Deutsch, Apr 18 2009

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..400

FORMULA

a(n) = 3 * A000313(n+2).

a(n) = (n/2)*A000240(n+1). - Zerinvary Lajos, Dec 18 2007, corrected Jul 09 2012

a(n) = n * (n+1) * (a(n-1)/(n-1) + (-1)^n/2) for n > 1 - Seiichi Manyama, Jun 24 2018

E.g.f.: exp(-x)*x^2*(3 - 2*x + x^2)/(2*(1 - x)^3). - Ilya Gutkovskiy, Jun 25 2018

a(n) ~ sqrt(Pi/2) * n^(n+5/2) / exp(n+1). - Amiram Eldar, Sep 20 2025

MATHEMATICA

a[n_] := Subfactorial[n]*Binomial[n + 1, 2];

Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Aug 18 2024 *)

CROSSREFS