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 A381164 #19 May 29 2025 02:33:41
%S A381164 1,121,113641,168508561,306213587881,624890127114721,
%T A381164 1374618918516663841,3187068298971939367561,7682172545187676630759081,
%U A381164 19079663136489248380982551201,48525227073661262262248690661841,125818607409307965748858681991235961,331488456546076036761442657285875590881
%N A381164 a(n) = Sum_{k=0..n} binomial(n,k)*(5*k)!/(k!)^5.
%C A381164 Calabi-Yau series number 79.
%H A381164 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 A381164 G.f.: hypergeom([1/5, 2/5, 3/5, 4/5], [1, 1, 1], 5^5*x/(1-x))/(1-x).
%F A381164 a(n) = hypergeom([1/5, 2/5, 3/5, 4/5, -n], [1, 1, 1, 1], -5^5).
%F A381164 a(n) == 1 (mod 120).
%F A381164 a(n) ~ 2^n * 3^(n+2) * 521^(n+2) / (5^(19/2) * Pi^2 * n^2). - _Vaclav Kotesovec_, May 29 2025
%t A381164 a[n_]:=Sum[Binomial[n, k](5k)!/k!^5, {k, 0, n}]; Array[a, 13, 0]
%Y A381164 Cf. A007318, A008978, A100734.
%Y A381164 Cf. A381161, A381162, A381163, A381165.
%K A381164 nonn
%O A381164 0,2
%A A381164 _Stefano Spezia_, Feb 15 2025