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 A202327 #21 May 19 2021 05:15:35
%S A202327 1,-1,1,0,-2,1,2,1,-3,1,-3,4,3,-4,1,-1,-10,5,6,-5,1,11,4,-21,4,10,-6,
%T A202327 1,-15,28,21,-35,0,15,-7,1,-13,-64,42,56,-50,-8,21,-8,1,77,9,-162,36,
%U A202327 114,-63,-21,28,-9,1,-86,230,135,-312,-15,198,-70,-40,36,-10,1
%N A202327 Triangle read by rows, T(n, k) is the coefficient of x^n in expansion of ((-1 - x + sqrt(1 + 2*x + 5*x^2)) /2)^k.
%F A202327 T(n, k) = (k/n) * Sum_{j=0..n} (-1)^(j-k) * binomial(n,j) * binomial(j,-n-k+2*j).
%F A202327 T(n, k) = binomial(n, k)*hypergeom([(k - n)/2, (k - n + 1)/2], [k + 2], -4)*(-1)^(n - k), assuming offset = 0. - _Peter Luschny_, May 19 2021
%e A202327 1;
%e A202327 -1, 1;
%e A202327 0, -2, 1;
%e A202327 2, 1, -3, 1;
%e A202327 -3, 4, 3, -4, 1;
%e A202327 -1, -10, 5, 6, -5, 1;
%e A202327 11, 4, -21, 4, 10, -6, 1;
%p A202327 # Assuming offset = 0.
%p A202327 T := (n,k) -> (-1)^(n-k)*binomial(n,k)*hypergeom([(k-n)/2, (k-n+1)/2], [k+2], -4): for n from 0 to 9 do seq(simplify(T(n, k)), k=0..n) od; # _Peter Luschny_, May 19 2021
%o A202327 (Maxima)
%o A202327 T(n,k):=(k*sum(binomial(j,-n-k+2*j)*(-1)^(j-k)*binomial(n,j),j,0,n))/n;
%Y A202327 Cf. A007440 (1st column), A108624 (row sums).
%K A202327 sign,tabl
%O A202327 1,5
%A A202327 _Vladimir Kruchinin_, Dec 17 2011
%E A202327 More terms from _Sean A. Irvine_, Mar 03 2021