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 A307911 #24 May 12 2021 03:07:18
%S A307911 1,-1,0,27,-416,5625,-74304,924385,-8626176,-48361131,7124800000,
%T A307911 -340421390199,13686496542720,-522760216822129,19658830846298112,
%U A307911 -735037915447265625,27218267709730979840,-980444996625142158435,32830565919734078521344,-889052809376495994642527
%N A307911 Coefficient of x^n in expansion of (1 - n*x - n*x^2)^n.
%C A307911 Also coefficient of x^n in the expansion of 1/sqrt(1 + 2*n*x + n*(n+4)*x^2).
%H A307911 Seiichi Manyama, <a href="/A307911/b307911.txt">Table of n, a(n) for n = 0..386</a>
%F A307911 a(n) = Sum_{k=0..floor(n/2)} (-n)^(n-k) * binomial(n,k) * binomial(n-k,k) = Sum_{k=0..floor(n/2)} (-n)^(n-k) * binomial(n,2*k) * binomial(2*k,k).
%F A307911 For n>0, a(n) = (-n)^n * Hypergeometric2F1(1/2 - n/2, -n/2, 1, -4/n). - _Vaclav Kotesovec_, May 12 2021
%t A307911 a[0] = 1; a[n_] := Sum[(-n)^(n-k) * Binomial[n, 2*k] * Binomial[2*k, k], {k, 0, Floor[n/2]}]; Array[a, 20, 0] // Flatten (* _Amiram Eldar_, May 12 2021 *)
%t A307911 Join[{1}, Table[(-n)^n*Hypergeometric2F1[1/2 - n/2, -n/2, 1, -4/n], {n, 1, 20}]] (* _Vaclav Kotesovec_, May 12 2021 *)
%o A307911 (PARI) {a(n) = polcoef((1-n*x-n*x^2)^n, n)}
%o A307911 (PARI) {a(n) = sum(k=0, n\2, (-n)^(n-k)*binomial(n, k)*binomial(n-k, k))}
%o A307911 (PARI) {a(n) = sum(k=0, n\2, (-n)^(n-k)*binomial(n, 2*k)*binomial(2*k, k))}
%Y A307911 Main diagonal of A307819.
%Y A307911 Cf. A092366, A307862.
%K A307911 sign
%O A307911 0,4
%A A307911 _Seiichi Manyama_, May 05 2019