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 A375365 #15 Aug 07 2025 12:03:19
%S A375365 1,-2,4,-3,6,-2,14,3,32,35,92,142,309,541,1061,1970,3770,7067,13423,
%T A375365 25328,47925,90546,171268,323704,612034,1157045,2187523,4135499,
%U A375365 7818493,14781207,27944635,52830674,99879267,188826659,356986436,674901081,1275934925,2412219595
%N A375365 Expansion of 1/( (1 + x)^2 * (1 - x^2*(1 + x)^3) ).
%H A375365 Harvey P. Dale, <a href="/A375365/b375365.txt">Table of n, a(n) for n = 0..1000</a>
%H A375365 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-2,0,5,10,10,5,1).
%F A375365 a(n) = -2*a(n-1) + 5*a(n-3) + 10*a(n-4) + 10*a(n-5) + 5*a(n-6) + a(n-7).
%F A375365 a(n) = Sum_{k=0..floor(n/2)} binomial(3*k-2,n-2*k).
%t A375365 CoefficientList[Series[1/((1+x)^2(1-x^2(1+x)^3)),{x,0,40}],x] (* or *) LinearRecurrence[{-2,0,5,10,10,5,1},{1,-2,4,-3,6,-2,14},40] (* _Harvey P. Dale_, Aug 07 2025 *)
%o A375365 (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1+x)^2*(1-x^2*(1+x)^3)))
%o A375365 (PARI) a(n) = sum(k=0, n\2, binomial(3*k-2, n-2*k));
%Y A375365 Cf. A375315, A375317, A375364.
%K A375365 sign
%O A375365 0,2
%A A375365 _Seiichi Manyama_, Aug 13 2024