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 A383916 #7 May 15 2025 08:18:10
%S A383916 1,1,68,22770,21143488,41904629550,151957171590144,910666718387157732,
%T A383916 8390164064875701321728,112583179357513548960803670,
%U A383916 2109812207969377622615440752640,53397692462483465346961668429307836,1775866125092261344436828225211633500160,75857512919848315654302238627976991244564300
%N A383916 a(n) = Sum_{k=0..n} binomial(2*n, k) * (n-k)^(3*n).
%F A383916 a(n) ~ 2^(2*n + 1/2) * r^(3*n + 1) * n^(3*n) / (sqrt(3 - r^2) * exp(3*n) * (1 - r^2)^n), where r = 0.92488761106894648930384927930334708844525256369797556858640... is the root of the equation (1 + r)/(1 - r) = exp(3/r).
%t A383916 Join[{1}, Table[Sum[Binomial[2*n, n-k]*k^(3*n), {k, 0, n}], {n, 1, 15}]]
%Y A383916 Cf. A032443, A345876, A209289/2, A383853, A383917.
%K A383916 nonn
%O A383916 0,3
%A A383916 _Vaclav Kotesovec_, May 15 2025