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 A381165 #14 May 29 2025 02:39:12
%S A381165 1,122,114126,169305620,307902541870,628881704226972,
%T A381165 1384648756554128604,3213280613371692112392,7752574653184355259506670,
%U A381165 19272593072633780827550508620,49062146831202726778631520779476,127331178560917294198014376933764792,335791906923524740189894975371277920796
%N A381165 a(n) = Sum_{k=0..n} binomial(2*n,n)*binomial(n, k)*(5*k)!/((k!)^3*(2*k)!).
%C A381165 Calabi-Yau series number 128.
%H A381165 S. Hassani, J.-M. Maillard, and N. Zenine, <a href="https://arxiv.org/abs/2502.05543">On the diagonals of rational functions: the minimal number of variables (unabridged version)</a>, arXiv:2502.05543 [math-ph], 2025. See p. 16.
%F A381165 G.f.: hypergeom([1/5, 2/5, 3/5, 4/5], [1, 1, 1], 5^5*x/(1-4*x))/sqrt(1-4*x).
%F A381165 a(n) = binomial(2*n,n)*hypergeom([1/5, 2/5, 3/5, 4/5, -n], [1/2, 1, 1, 1], -5^5/4).
%F A381165 a(n) ~ 3^(n + 3/2) * 7^(n + 3/2) * 149^(n +3/2) / (4 * 5^7 * Pi^2 * n^2). - _Vaclav Kotesovec_, May 29 2025
%t A381165 a[n_]:=Sum[Binomial[2n,n]Binomial[n, k](5k)!/((k!)^3*(2k)!), {k, 0, n}]; Array[a, 13, 0]
%Y A381165 Cf. A000442, A000984, A007318, A010050, A100734.
%Y A381165 Cf. A381161, A381162, A381163, A381164.
%K A381165 nonn
%O A381165 0,2
%A A381165 _Stefano Spezia_, Feb 15 2025