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Numerator of Sum_{k=0..n} 1/binomial(n,k)^4.
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%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