A128152 Numerator of Sum_{k=0..n} 1/binomial(n,k)^4.

1, 2, 33, 164, 20825, 10017, 25940593, 34743416, 3074035689, 672229195, 13443874324243, 431453199593, 53678600587865227, 33768054132971557, 813464644344955, 748569723383876272, 67454811525665973337193

Offset: 0

Author

Alexander Adamchuk, May 10 2007

Keywords

• frac
• nonn

Comments

p^k divides a(p^k-1) for prime p and integer k > 0. p divides a(p-2) for prime p > 5.

Links

• Eric Weisstein's World of Mathematics, Binomial Sums.

Crossrefs

Cf. A046825 (numerator of Sum_{k=0..n} 1/C(n, k)).

Cf. A100516 (numerator of Sum_{k=0..n} 1/C(n, k)^2).

Cf. A100518 (numerator of Sum_{k=0..n} 1/C(n, k)^3).

Programs

Mathematica

Table[ Numerator[ Sum[ 1 / Binomial[n,k]^4, {k,0,n} ] ], {n,0,50} ]

Formula

a(n) = numerator(Sum_{k=0..n} 1/binomial(n,k)^4).