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 A027823 #19 Feb 04 2022 06:10:32
%S A027823 462,6468,48048,252252,1051050,3699696,11435424,31855824,81477396,
%T A027823 193993800,434546112,923410488,1873980108,3651858672,6864396000,
%U A027823 12493200720,22086194130,38030772780,63935791920,105157552500,169513974630,268241893920,417265168320
%N A027823 a(n) = 77*(n+1)*binomial(n+6,11).
%C A027823 Number of 18-subsequences of [ 1, n ] with just 6 contiguous pairs.
%H A027823 T. D. Noe, <a href="/A027823/b027823.txt">Table of n, a(n) for n = 5..1000</a>
%H A027823 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F A027823 G.f.: 462*(1+x)*x^5/(1-x)^13.
%F A027823 a(n) = C(n+1, 6)*C(n+6, 6). - _Zerinvary Lajos_, Jun 08 2005; corrected by _R. J. Mathar_, Feb 13 2016
%F A027823 From _Amiram Eldar_, Feb 04 2022: (Start)
%F A027823 Sum_{n>=5} 1/a(n) = 10446403/176400 - 6*Pi^2.
%F A027823 Sum_{n>=5} (-1)^(n+1)/a(n) = 3*Pi^2 - 82899/2800. (End)
%t A027823 Table[77(n+1) Binomial[n+6,11],{n,5,40}] (* or *) LinearRecurrence[{13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{462,6468,48048,252252,1051050,3699696,11435424,31855824,81477396,193993800,434546112,923410488,1873980108},30] (* _Harvey P. Dale_, Oct 20 2016 *)
%Y A027823 Cf. A062190.
%K A027823 nonn,easy
%O A027823 5,1
%A A027823 Thi Ngoc Dinh (via _R. K. Guy_)