This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060008 #30 Dec 25 2024 15:50:06
%S A060008 0,0,0,0,9,45,135,315,630,1134,1890,2970,4455,6435,9009,12285,16380,
%T A060008 21420,27540,34884,43605,53865,65835,79695,95634,113850,134550,157950,
%U A060008 184275,213759,246645,283185,323640,368280,417384,471240,530145,594405
%N A060008 a(n) = 9*binomial(n,4) = 3n*(n-1)*(n-2)*(n-3)/8.
%C A060008 Number of permutations of n letters where exactly four change position.
%H A060008 Harry J. Smith, <a href="/A060008/b060008.txt">Table of n, a(n) for n = 0..1000</a>
%H A060008 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A060008 Equals 3*A050534. - _Zerinvary Lajos_, Feb 12 2007
%F A060008 G.f.: 9*x^4/(1-x)^5. - _Colin Barker_, Jul 02 2012
%F A060008 From _Amiram Eldar_, Jul 19 2022: (Start)
%F A060008 Sum_{n>=4} 1/a(n) = 4/27.
%F A060008 Sum_{n>=4} (-1)^n/a(n) = 32*log(2)/9 - 64/27. (End)
%e A060008 a(6) = 135 since there are 15 ways to choose the four points that move and 9 ways to move them and 15*9 = 135.
%t A060008 9*Binomial[Range[0,40],4] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,0,0,0,9},40] (* _Harvey P. Dale_, Jun 09 2014 *)
%o A060008 (PARI) a(n) = { 3*n*(n - 1)*(n - 2)*(n - 3)/8 } \\ _Harry J. Smith_, Jul 01 2009
%Y A060008 For changing 0, 1, 2, 3, 4, 5, n-4, n elements see A000012, A000004, A000217 (offset), A007290, A060008, A060836, A000475, A000166. Also see A000332, A008290.
%Y A060008 A diagonal of A008291.
%K A060008 easy,nonn
%O A060008 0,5
%A A060008 _Henry Bottomley_, Mar 16 2001