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 A382642 #19 Apr 10 2025 03:25:19
%S A382642 1,6,112,2784,79716,2478936,81369856,2774798592,97345792804,
%T A382642 3490750940376,127377525333312,4714499194430592,176563416839871504,
%U A382642 6678628406445775968,254781841509308692992,9791397137378344986624,378713818451270226094884,14731112080159997036570328
%N A382642 a(n) = Sum_{k=0..n} (binomial(n,k) * binomial(n+k,k))^2 * 2^(n-k).
%C A382642 Diagonal of the rational function 1 / (1 - y - z - x*y - z*w - 2*x*z - x*y*w - 2*x*y*z*w).
%F A382642 a(n) ~ sqrt(6 + 4*sqrt(2) + sqrt(137/2 + 97/sqrt(2))) * (10 + 8*sqrt(2) + 4*sqrt(14 + 10*sqrt(2)))^n / (4 * Pi^(3/2) * n^(3/2)). - _Vaclav Kotesovec_, Apr 08 2025
%t A382642 Table[Sum[(Binomial[n, k] Binomial[n + k, k])^2 2^(n - k), {k, 0, n}], {n, 0, 17}]
%t A382642 Table[2^n HypergeometricPFQ[{-n, -n, n + 1, n + 1}, {1, 1, 1}, 1/2], {n, 0, 17}]
%t A382642 Table[SeriesCoefficient[1/(1 - y - z - x y - z w - 2 x z - x y w - 2 x y z w), {x, 0, n}, {y, 0, n}, {z, 0, n}, {w, 0, n}], {n, 0, 17}]
%Y A382642 Cf. A001850, A005259, A069835, A382405.
%K A382642 nonn
%O A382642 0,2
%A A382642 _Ilya Gutkovskiy_, Apr 08 2025