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 A027767 #32 Jan 30 2022 04:17:24
%S A027767 7,64,324,1200,3630,9504,22308,48048,96525,183040,330616,572832,
%T A027767 957372,1550400,2441880,3751968,5638611,8306496,12017500,17102800,
%U A027767 23976810,33153120,45262620,61074000,81516825,107707392,140977584,182906944,235358200,300516480,380932464
%N A027767 a(n) = (n+1)*binomial(n+1,7).
%C A027767 Number of 9-subsequences of [ 1, n ] with just 1 contiguous pair.
%C A027767 229*a(n) is the number of permutations of (n+1) symbols that 7-commute with an (n+1)-cycle (see A233440 for definition), where 229 = A000757(7). - _Luis Manuel Rivera MartÃnez_, Feb 07 2014
%H A027767 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A027767 G.f.: (7+x)*x^6/(1-x)^9.
%F A027767 From _Amiram Eldar_, Jan 30 2022: (Start)
%F A027767 Sum_{n>=6} 1/a(n) = 7*Pi^2/6 - 6811/600.
%F A027767 Sum_{n>=6} (-1)^n/a(n) = 7*Pi^2/12 + 2912*log(2)/15 - 252343/1800. (End)
%t A027767 Table[(n+1)Binomial[n+1,7],{n,6,40}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{7,64,324,1200,3630,9504,22308,48048,96525},30] (* _Harvey P. Dale_, Mar 13 2016 *)
%Y A027767 Cf. A000757, A233440.
%K A027767 nonn,easy
%O A027767 6,1
%A A027767 Thi Ngoc Dinh (via _R. K. Guy_)
%E A027767 Incorrect formula deleted by _R. J. Mathar_, Feb 13 2016