A065087 - OEIS

%I #37 Aug 18 2024 14:10:42

%S 0,0,3,12,90,660,5565,51912,533988,6007320,73422855,969181620,

%T 13744757598,208462156812,3367465610145,57727981888080,

%U 1046800738237320,20020064118788592,402756584036805963,8502638996332570140,187953072550509445410,4341715975916768188740

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

%C 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

%H Seiichi Manyama, <a href="/A065087/b065087.txt">Table of n, a(n) for n = 0..400</a>

%F a(n) = (n/2)*A000240(n+1). - _Zerinvary Lajos_, Dec 18 2007, corrected Jul 09 2012

%F a(n) = n * (n+1) * (a(n-1)/(n-1) + (-1)^n/2) for n > 1 - _Seiichi Manyama_, Jun 24 2018

%F E.g.f.: exp(-x)*x^2*(3 - 2*x + x^2)/(2*(1 - x)^3). - _Ilya Gutkovskiy_, Jun 25 2018

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

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Aug 18 2024 *)

%Y Equals 3 * A000313(n+2).

%Y Cf. A000166, A000240, A000387, A305730.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Nov 10 2001