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 A138331 #19 Sep 08 2022 08:45:33
%S A138331 -16,128,-560,1792,-4704,10752,-22176,42240,-75504,128128,-208208,
%T A138331 326144,-495040,731136,-1054272,1488384,-2062032,2808960,-3768688,
%U A138331 4987136,-6517280,8419840,-10764000,13628160,-17100720,21280896,-26279568,32220160,-39239552
%N A138331 a(n) = C(n+5, 5)*(n+3)*(-1)^(n+1)*16/3.
%C A138331 Fourth column of the triangle defined in A123588, seventh column of the triangle defined in A123583.
%H A138331 Robert Israel, <a href="/A138331/b138331.txt">Table of n, a(n) for n = 0..10000</a>
%H A138331 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A138331 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-7,-21,-35,-35,-21,-7,-1).
%F A138331 a(n) = coefficient of x^6 in the polynomial 1 - T_(n+3)(x)^2, where T_n(x) is the n-th Chebyshev polynomial of the first kind.
%F A138331 G.f.: 16*(x-1)/(x+1)^7.
%F A138331 a(n) = (-1)^(n+1)*16*A040977(n).
%F A138331 a(n) = a(-n-5). - _Bruno Berselli_, Sep 13 2011
%p A138331 seq(binomial(n+5, 5)*(n+3)*(-1)^(n+1)*16/3, n=0..40); # _Robert Israel_, Oct 26 2017
%t A138331 LinearRecurrence[{-7,-21,-35,-35,-21,-7,-1},{-16,128,-560,1792,-4704,10752,-22176},30] (* _Harvey P. Dale_, May 27 2017 *)
%o A138331 (Magma) [ Binomial(n+5, 5)*(n+3)*(-1)^(n+1)*16/3: n in [0..28] ];
%o A138331 (Magma) k:=3; [ Coefficients(1-ChebyshevT(n+k)^2)[2*k+1]: n in [0..28] ];
%o A138331 (PARI) for(n=0,28,print1(polcoeff(taylor(16*(x-1)/(x+1)^7,x),n),","));
%Y A138331 Cf. A007318 (Pascal's triangle), A123588, A123583, A040977.
%K A138331 sign,easy
%O A138331 0,1
%A A138331 _Klaus Brockhaus_, Mar 15 2008