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 A027778 #31 Feb 01 2022 02:34:50
%S A027778 10,75,315,980,2520,5670,11550,21780,38610,65065,105105,163800,247520,
%T A027778 364140,523260,736440,1017450,1382535,1850695,2443980,3187800,4111250,
%U A027778 5247450,6633900,8312850,10331685,12743325,15606640,18986880,22956120,27593720,32986800,39230730
%N A027778 a(n) = 5*(n+1)*binomial(n+2, 5)/2.
%C A027778 Number of 8-subsequences of [ 1, n ] with just 2 contiguous pairs.
%H A027778 Michael De Vlieger, <a href="/A027778/b027778.txt">Table of n, a(n) for n = 3..10000</a>
%H A027778 Ronald Orozco López, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Orozco/orozco5.html">Solution of the Differential Equation y^(k)= e^(a*y), Special Values of Bell Polynomials and (k,a)-Autonomous Coefficients</a>, Journal of Integer Sequences, Vol. 24 (2021), Article 21.8.6; <a href="https://www.researchgate.net/publication/350397609_Solution_of_the_Differential_Equation_ykeay_Special_Values_of_Bell_Polynomials_and_ka-Autonomous_Coefficients">ResearchGate link</a>.
%H A027778 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A027778 G.f.: 5*x^3*(2+x)/(1-x)^7.
%F A027778 a(n) = binomial(n+1, 4)*binomial(n+2, 2). - _Zerinvary Lajos_, Apr 28 2005, corrected by _R. J. Mathar_, Feb 13 2016
%F A027778 From _Amiram Eldar_, Feb 01 2022: (Start)
%F A027778 Sum_{n>=3} 1/a(n) = 239/18 - 4*Pi^2/3.
%F A027778 Sum_{n>=3} (-1)^(n+1)/a(n) = 2*Pi^2/3 + 64*log(2)/3 - 383/18. (End)
%t A027778 DeleteCases[CoefficientList[Series[5 x^3*(2 + x)/(1 - x)^7, {x, 0, 24}], x], 0] (* _Michael De Vlieger_, Jul 16 2021 *)
%Y A027778 Not equal to 5*A005715(n+1)/2.
%K A027778 nonn,easy
%O A027778 3,1
%A A027778 Thi Ngoc Dinh (via _R. K. Guy_)