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 A320624 #8 Oct 26 2018 00:56:39 %S A320624 1,2,4,32,98,1034,3484,41582,1868198,6751460,330246410,4522217312, %T A320624 16829506610,235344648416,12559206444236,683534482499900, %U A320624 2599887148071402,144419015585768252,2117118216002111198,8120930597438173620 %N A320624 a(n) = (A006134((prime(n)-1)/2) - Legendre(prime(n), 3))/prime(n). %C A320624 a(n) is always an integer. %C A320624 Primes p such that p^2 divides A006134((p-1)/2) - Legendre(p, 3) are p = 103, ... What's the next? %F A320624 a(2) = (binomial(0, 0) + binomial(2, 1))/3 = 3/3 = 1. %F A320624 a(3) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + 1)/5 = 10/5 = 2. %F A320624 a(4) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + binomial(6, 3) - 1)/7 = 28/7 = 4. %o A320624 (PARI) A006134(n) = sum(k=0, n, binomial(2*k,k)) %o A320624 a(n) = my(p=prime(n)); (A006134((p-1)/2) - kronecker(p,3))/p %Y A320624 Cf. A006134, A102283, A320626. %K A320624 nonn %O A320624 2,2 %A A320624 _Jianing Song_, Oct 18 2018