%I #8 Jun 13 2021 03:22:29
%S 1,2,33,164,20825,10017,25940593,34743416,3074035689,672229195,
%T 13443874324243,431453199593,53678600587865227,33768054132971557,
%U 813464644344955,748569723383876272,67454811525665973337193
%N Numerator of Sum_{k=0..n} 1/binomial(n,k)^4.
%C p^k divides a(p^k-1) for prime p and integer k > 0. p divides a(p-2) for prime p > 5.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>.
%F a(n) = numerator(Sum_{k=0..n} 1/binomial(n,k)^4).
%t Table[ Numerator[ Sum[ 1 / Binomial[n,k]^4, {k,0,n} ] ], {n,0,50} ]
%Y Cf. A046825 (numerator of Sum_{k=0..n} 1/C(n, k)).
%Y Cf. A100516 (numerator of Sum_{k=0..n} 1/C(n, k)^2).
%Y Cf. A100518 (numerator of Sum_{k=0..n} 1/C(n, k)^3).
%K frac,nonn
%O 0,2
%A _Alexander Adamchuk_, May 10 2007