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 A268589 #16 Aug 27 2025 18:42:16
%S A268589 12,2364,43500,20791626,514377588,373783661124,9888937247184828,
%T A268589 312285010312512084,11167980739981519994382,
%U A268589 13185583459205473525798038,462369843775374621687338484,588608385261717115044847555476,28758863221144089886068560242560564,1508365481231852329668720928730586740868
%N A268589 a(n) = (2*C(3p,p) - 9*C(2p,p) + 12) / p^5, where p = prime(n).
%C A268589 a(n) is an integer for all n>=4, see A268512.
%H A268589 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.
%t A268589 Table[(2*Binomial[3p,p]-9*Binomial[2p,p]+12)/p^5,{p,Prime[Range[4,20]]}] (* _Harvey P. Dale_, Aug 27 2025 *)
%o A268589 (PARI) { A268589(n) = my(p=prime(n)); (12 - 9*binomial(2*p,p) + 2*binomial(3*p,p))/p^5; }
%Y A268589 Cf. A268512, A087754, A268590.
%K A268589 nonn,changed
%O A268589 4,1
%A A268589 _Max Alekseyev_, Feb 07 2016