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 A382849 #6 Apr 09 2025 05:40:07
%S A382849 1,3,1,-357,-6999,-62997,444529,27783003,508019689,3206511003,
%T A382849 -89889084999,-3274278527517,-49395223500999,-66079827133317,
%U A382849 16197028704290001,433384098559415643,4988878584849669609,-35687369703800052357,-2815548294132454060151,-58942279760573467233357
%N A382849 a(n) = Sum_{k=0..n} (-1)^(n-k) * (binomial(n,k) * binomial(n+k,k))^2.
%C A382849 Diagonal of the rational function 1 / (1 - y + z + x*y + z*w + x*z + x*y*w + x*y*z*w).
%t A382849 Table[Sum[(-1)^(n - k) (Binomial[n, k] Binomial[n + k, k])^2, {k, 0, n}], {n, 0, 19}]
%t A382849 Table[(-1)^n HypergeometricPFQ[{-n, -n, n + 1, n + 1}, {1, 1, 1}, -1], {n, 0, 19}]
%t A382849 Table[SeriesCoefficient[1/(1 - y + z + x y + z w + x z + x y w + x y z w), {x, 0, n}, {y, 0, n}, {z, 0, n}, {w, 0, n}], {n, 0, 19}]
%Y A382849 Cf. A005258, A005259, A126869, A176335, A228304, A382848.
%K A382849 sign
%O A382849 0,2
%A A382849 _Ilya Gutkovskiy_, Apr 06 2025