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 A365083 #11 Aug 21 2023 08:23:07
%S A365083 1,1,-3,3,5,-22,27,28,-163,235,134,-1188,1983,408,-8504,16320,-1551,
%T A365083 -59659,131507,-46683,-408806,1040147,-612380,-2721835,8088003,
%U A365083 -6523626,-17457420,61883839,-62900496,-106248240,466069760,-571001695,-595520019,3454539427
%N A365083 G.f. satisfies A(x) = 1 + x*A(x) / (1 + x)^4.
%H A365083 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-6,-4,-1).
%F A365083 G.f.: A(x) = 1/( 1 - x/(1+x)^4 ).
%F A365083 a(n) = -3*a(n-1) - 6*a(n-2) - 4*a(n-3) - a(n-4) for n > 4.
%F A365083 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n+3*k-1,n-k).
%t A365083 LinearRecurrence[{-3, -6, -4, -1}, {1, 1, -3, 3, 5}, 1 + 33] (* _Robert P. P. McKone_, Aug 21 2023 *)
%o A365083 (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n+3*k-1, n-k));
%Y A365083 Cf. A106510, A127896, A365084.
%Y A365083 Cf. A055991.
%K A365083 sign,easy
%O A365083 0,3
%A A365083 _Seiichi Manyama_, Aug 21 2023