OFFSET
2,1
COMMENTS
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.
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.
LINKS
Eric Weisstein's World of Mathematics, Pascal's Triangle
Eric Weisstein's World of Mathematics, Binomial Sums
MATHEMATICA
Table[(Sum[Binomial[m, k]^(Prime[n] - 1), {m, 0, Prime[n] - 1}, {k, 0, m}])/Prime[n], {n, 2, 10}]
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Apr 04 2012
STATUS
approved