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 A320626 #8 Oct 26 2018 02:55:10 %S A320626 1,1,4,26,2074,21660,2804068,33847970,5345496688,12201269878660, %T A320626 165029257057602,433037204976615540,85637003420093445994, %U A320626 1215603499085916654728,248871244937134915010626,753881874165723132009014662,2359161060012378685209851991166 %N A320626 a(n) = (A006134(prime(n)-1) - Legendre(prime(n), 3))/prime(n)^2. %C A320626 a(n) is always an integer. %C A320626 Are there any primes p such that p^3 divides A006134(p-1) - Legendre(p, 3)? %e A320626 a(1) = (binomial(0, 0) + binomial(2, 1) + 1)/4 = 4/4 = 1. %e A320626 a(2) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2))/9 = 9/9 = 1. %e A320626 a(3) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + binomial(6, 3) + binomial(8, 4) + 1)/25 = 100/25 = 4. %o A320626 (PARI) A006134(n) = sum(k=0,n,binomial(2*k,k)) %o A320626 a(n) = my(p=prime(n)); (A006134(p-1) - kronecker(p,3))/p^2 %Y A320626 Cf. A006134, A102283, A320624. %K A320626 nonn %O A320626 1,3 %A A320626 _Jianing Song_, Oct 18 2018