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 A268590 #12 Jan 12 2025 04:55:35
%S A268590 984,27780,32144568,1269360060,2470299005220,316528131552725460,
%T A268590 17262503097511844124,3329177348896984023277536,
%U A268590 12461979236231507288981559840,783882118494853605112684502280,3251723952081272231067929776337100,959689034437453143807696476144553320100
%N A268590 a(n) = (3*C(4p,p) - 20*C(3p,p) + 54*C(2p,p) - 60) / p^7, where p = prime(n).
%C A268590 a(n) is an integer for all n>=5, see A268512.
%H A268590 R. R. Aidagulov and M. A. Alekseyev. On p-adic approximation of sums of binomial coefficients. Journal of Mathematical Sciences 233:5 (2018), 626-634. doi:<a href="http://doi.org/10.1007/s10958-018-3948-0">10.1007/s10958-018-3948-0</a>; <a href="http://arxiv.org/abs/1602.02632">arXiv preprint</a>, arXiv:1602.02632 [math.NT], 2016-2018.
%o A268590 (PARI) { A268590(n) = my(p=prime(n)); (-60 + 54*binomial(2*p,p) - 20*binomial(3*p,p) + 3*binomial(4*p,p))/p^7; }
%Y A268590 Cf. A268512, A087754, A268589.
%K A268590 nonn
%O A268590 5,1
%A A268590 _Max Alekseyev_, Feb 07 2016