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 A181990 #23 Feb 16 2025 08:33:13
%S A181990 3,399,12708885,124515078454872901983423,
%T A181990 39212583445587381894247266262023061,
%U A181990 43487633454143579523135045521112077473364484383507327790688372131,157851796824901989964381293031623545741924564754192453966085327785455257503133278729
%N A181990 a(n) = Sum_{0 <= k <= m < p} (binomial(m, k)^(p-1))/p, where p is the n-th prime.
%C A181990 a(n) is a sum of all elements in the first p rows of Pascal's triangle each raised to the (p-1) power and divided by p, where p is the n-th prime.
%C A181990 For p = 3 and 7 (and their powers like 3, 9, 27, ... and 7, 49, ...) the sums of all elements in n = p^k top rows of Pascal's triangle each raised to the (n-1) = (p^k-1) power are divisible by n^2 = p^(2k) for all k > 0.
%H A181990 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PascalsTriangle.html">Pascal's Triangle</a>
%H A181990 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>
%t A181990 Table[(Sum[Binomial[m, k]^(Prime[n] - 1), {m, 0, Prime[n] - 1}, {k, 0, m}])/Prime[n], {n, 2, 10}]
%o A181990 (PARI) a(n) = my(p=prime(n)); sum(m=0, p-1, sum(k=0, m, binomial(m,k)^(p-1))/p); \\ _Michel Marcus_, Dec 03 2018
%Y A181990 Cf. A007318, A006134, A083096, A066796, A083097, A081601, A010060, A122485, A167912.
%K A181990 nonn
%O A181990 2,1
%A A181990 _Alexander Adamchuk_, Apr 04 2012