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 A027768 #36 Jan 30 2022 04:23:57
%S A027768 8,81,450,1815,5940,16731,42042,96525,205920,413270,787644,1436058,
%T A027768 2519400,4273290,7034940,11277222,17651304,27039375,40619150,59942025,
%U A027768 87026940,124472205,175587750,244550475,336585600,458177148,617310936,823753700,1089372240
%N A027768 a(n) = (n+1)*binomial(n+1,8).
%C A027768 Number of 10-subsequences of [ 1, n ] with just 1 contiguous pair.
%C A027768 1625*a(n) is the number of permutations of (n+1) symbols that 8-commute with an (n+1)-cycle (see A233440 for definition), where 1625 = A000757(8). - _Luis Manuel Rivera MartÃnez_, Feb 07 2014
%H A027768 Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%H A027768 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A027768 G.f.: (8+x)*x^7/(1-x)^10.
%F A027768 From _Amiram Eldar_, Jan 30 2022: (Start)
%F A027768 Sum_{n>=7} 1/a(n) = 48877/3675 - 4*Pi^2/3.
%F A027768 Sum_{n>=7} (-1)^(n+1)/a(n) = 2*Pi^2/3 + 38656*log(2)/105 - 2884681/11025. (End)
%t A027768 Table[(n+1)Binomial[n+1,8],{n,7,40}] (* _Harvey P. Dale_, Jul 08 2017 *)
%o A027768 (PARI) a(n) = (n+1)*binomial(n+1, 8); \\ _Michel Marcus_, Jan 31 2014
%Y A027768 Cf. A000757, A233440.
%K A027768 nonn,easy
%O A027768 7,1
%A A027768 Thi Ngoc Dinh (via _R. K. Guy_)
%E A027768 Incorrect formula deleted . - _R. J. Mathar_, Feb 13 2016