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 A027772 #30 Jan 30 2022 04:22:36
%S A027772 12,169,1274,6825,29120,105196,334152,957372,2519400,6172530,14226212,
%T A027772 31097794,64899744,130007500,251100200,469364220,851809140,1504982115,
%U A027772 2594796750,4374736275,7225370880,11708971560,18644037360,29205813000,45060397200,68541870852
%N A027772 a(n) = (n+1)*binomial(n+1,12).
%C A027772 Number of 14-subsequences of [ 1, n ] with just 1 contiguous pair.
%H A027772 T. D. Noe, <a href="/A027772/b027772.txt">Table of n, a(n) for n = 11..1000</a>
%H A027772 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 A027772 <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
%F A027772 G.f.: (12+x)*x^11/(1-x)^14.
%F A027772 From _Amiram Eldar_, Jan 30 2022: (Start)
%F A027772 Sum_{n>=11} 1/a(n) = 634871227/32016600 - 2*Pi^2.
%F A027772 Sum_{n>=11} (-1)^(n+1)/a(n) = Pi^2 + 5869568*log(2)/1155 - 113091604693/32016600. (End)
%t A027772 Table[(n+1)Binomial[n+1,12],{n,11,40}] (* or *) LinearRecurrence[{14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1},{12,169,1274,6825,29120,105196,334152,957372,2519400,6172530,14226212,31097794,64899744,130007500},30] (* _Harvey P. Dale_, Mar 13 2018 *)
%K A027772 nonn,easy
%O A027772 11,1
%A A027772 Thi Ngoc Dinh (via _R. K. Guy_)