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 A357960 #7 Nov 06 2022 07:50:49
%S A357960 729,147018378125,20917910914764786689697,
%T A357960 24148107115850058575342740485778125,
%U A357960 79477722547796770983047586179643766765851375729,492664048531500749211923278756418311980637289373757041378125,4671227340507161302417161873394448514470099313382652883508175438056640625
%N A357960 a(n) = A005259(n-1)^5 * A005258(n)^6.
%C A357960 Conjectures:
%C A357960 1) a(p) == a(1) (mod p^5) for all primes p >= 3 (checked up to p = 271).
%C A357960 2) a(p^r) == a(p^(r-1)) ( mod p^(3*r+3) ) for r >= 2 and for all primes p >= 3. These are stronger supercongruences than those satisfied separately by the two types of Apéry numbers A005258 and A005259.
%F A357960 a(n) = ( Sum_{k = 0..n-1} binomial(n-1,k)^2*binomial(n+k-1,k)^2 )^5 * ( Sum_{k = 0..n} binomial(n,k)^2*binomial(n+k,k) )^6.
%F A357960 a(n*p^r) == a(n*p^(r-1)) ( mod p^(3*r) ) for positive integers n and r and for all primes p >= 5.
%p A357960 seq( add(binomial(n-1,k)^2*binomial(n+k-1,k)^2, k = 0..n-1)^5 * add(binomial(n, k)^2*binomial(n+k,k), k = 0..n)^6, n = 1..20);
%Y A357960 Cf. A005258, A005259, A212334, A352655, A357567, A357956, A357957, A357958, A357959.
%K A357960 nonn,easy
%O A357960 1,1
%A A357960 _Peter Bala_, Oct 25 2022