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 A383853 #7 May 13 2025 00:57:57
%S A383853 1,1,260,556032,4641176128,106519579045760,5472276566891956224,
%T A383853 549375993583284180705280,97867116732573493470161420288,
%U A383853 28783909470167571938915053763592192,13216052972619446942074113385580542689280,9058922175695195359062480694771506779050213376
%N A383853 a(n) = Sum_{k=0..n} binomial(2*n, k) * (n-k)^(4*n).
%F A383853 a(n) = Sum_{k=0..n} binomial(2*n, n+k) * k^(4*n).
%F A383853 a(n) ~ 4^n * r^(4*n+1) * n^(4*n) / (sqrt(2 - r^2) * (1 - r^2)^n * exp(4*n)), where r = 0.9683644349844134852843167967986294187258222293516... is the root of the equation (1+r)/(1-r) = exp(4/r).
%t A383853 Join[{1}, Table[Sum[Binomial[2*n, k]*(n-k)^(4*n), {k, 0, n}], {n, 1, 12}]] (* or *)
%t A383853 Join[{1}, Table[Sum[Binomial[2*n, n+k]*k^(4*n), {k, 0, n}], {n, 1, 12}]]
%Y A383853 Cf. A209289, A298851, A345876.
%K A383853 nonn
%O A383853 0,3
%A A383853 _Vaclav Kotesovec_, May 12 2025