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 A027774 #26 Jan 30 2022 04:22:52
%S A027774 14,225,1920,11560,55080,220932,775200,2441880,7034940,18795370,
%T A027774 47070144,111435000,251100200,541574100,1123264800,2249204040,
%U A027774 4362680250,8220658275,15085939200,27020703600,47327171760,81198579000,136666699200,225962211600,367443055800
%N A027774 a(n) = (n+1)*binomial(n+1,14).
%C A027774 Number of 16-subsequences of [ 1, n ] with just 1 contiguous pair.
%H A027774 T. D. Noe, <a href="/A027774/b027774.txt">Table of n, a(n) for n = 13..1000</a>
%H A027774 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 A027774 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
%F A027774 G.f.: (14+x)*x^13/(1-x)^16.
%F A027774 From _Amiram Eldar_, Jan 30 2022: (Start)
%F A027774 Sum_{n>=13} 1/a(n) = 107159834863/4637833200 - 7*Pi^2/3.
%F A027774 Sum_{n>=13} (-1)^(n+1)/a(n) = 7*Pi^2/6 + 125673472*log(2)/6435 - 62835162326017/4637833200. (End)
%t A027774 Table[(n+1)Binomial[n+1,14],{n,13,40}] (* _Harvey P. Dale_, Nov 04 2017 *)
%K A027774 nonn,easy
%O A027774 13,1
%A A027774 Thi Ngoc Dinh (via _R. K. Guy_)