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 A307862 #28 May 31 2020 21:58:09
%S A307862 1,1,-3,-17,49,651,-1259,-38023,26433,2969299,2225101,-289389891,
%T A307862 -692529551,33718183045,143578976997,-4559187616649,-29119975483135,
%U A307862 699788001188403,6188699469443869,-119828491083854707,-1404529670244379599,22563726025297759345,341997845736800473397
%N A307862 Coefficient of x^n in (1 + x - n*x^2)^n.
%C A307862 Also coefficient of x^n in the expansion of 1/sqrt(1 - 2*x + (1+4*n)*x^2).
%H A307862 Seiichi Manyama, <a href="/A307862/b307862.txt">Table of n, a(n) for n = 0..500</a>
%F A307862 a(n) = Sum_{k=0..floor(n/2)} (-n)^k * binomial(n,k) * binomial(n-k,k).
%F A307862 a(n) = Sum_{k=0..floor(n/2)} (-n)^k * binomial(n,2*k) * binomial(2*k,k).
%F A307862 a(n) = n! * [x^n] exp(x) * BesselI(0,2*sqrt(-n)*x). - _Ilya Gutkovskiy_, May 31 2020
%F A307862 a(n) = Hypergeometric2F1(-n/2, (1-n)/2; 1; -4*n). - _G. C. Greubel_, May 31 2020
%p A307862 A307862:= n -> simplify(hypergeom([-n/2, (1-n)/2], [1], -4*n));
%p A307862 seq(A307862(n), n = 0..30); # _G. C. Greubel_, May 31 2020
%t A307862 a[n_]:= SeriesCoefficient[(1 +x -n*x^2)^n, {x,0,n}]; Table[a[n], {n,0,30}] (* _G. C. Greubel_, May 31 2020 *)
%o A307862 (PARI) {a(n) = polcoef((1+x-n*x^2)^n, n)}
%o A307862 (PARI) {a(n) = sum(k=0, n\2, (-n)^k*binomial(n, k)*binomial(n-k, k))}
%o A307862 (PARI) {a(n) = sum(k=0, n\2, (-n)^k*binomial(n, 2*k)*binomial(2*k, k))}
%o A307862 (Sage) [ hypergeometric([-n/2, (1-n)/2], [1], -4*n).simplify_hypergeometric() for n in (0..30)] # _G. C. Greubel_, May 31 2020
%Y A307862 Main diagonal of A307860.
%Y A307862 Cf. A002426, A187018, A307885.
%K A307862 sign
%O A307862 0,3
%A A307862 _Seiichi Manyama_, May 02 2019