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 A381163 #18 May 29 2025 02:28:10
%S A381163 1,49,15217,7437505,4444068913,2978797867489,2151085262277121,
%T A381163 1636678166183569873,1294384621280668799665,1054623536679756097536097,
%U A381163 879831837105310233485202337,748258333337818719124808979313,646586399881218539235007860940609,566284969531710881501724274920081265
%N A381163 a(n) = Sum_{k=0..n} binomial(n,k)*(4*k)!*(2*k)!/(k!)^6.
%C A381163 Calabi-Yau series number 76.
%H A381163 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 pp. 15-16.
%F A381163 G.f.: hypergeom([1/2, 1/2, 1/4, 3/4], [1, 1, 1], 2^10*x/(1-x))/(1-x).
%F A381163 a(n) = hypergeom([1/4, 1/2, 1/2, 3/4, -n], [1, 1, 1, 1], -2^10).
%F A381163 a(n) == 1 (mod 48).
%F A381163 a(n) ~ 5^(2*n+4) * 41^(n+2) / (2^(41/2) * Pi^2 * n^2). - _Vaclav Kotesovec_, May 29 2025
%t A381163 a[n_]:=Sum[Binomial[n,k](4k)!(2k)!/k!^6,{k,0,n}]; Array[a,14,0]
%Y A381163 Cf. A007318, A010050, A100733, A307618.
%Y A381163 Cf. A381161, A381162, A381164, A381165.
%K A381163 nonn
%O A381163 0,2
%A A381163 _Stefano Spezia_, Feb 15 2025