A122184 Numerator of Sum_{k=0..2n} (-1)^k/C(2n,k)^3.

1, 15, 1705, 47789, 1369377, 213162301, 43005554527, 14505995375, 23869750002797, 2384790127843063, 624724994927411, 24386251366041479501, 2042595777439018142725, 11191251831905709132993

Offset: 0

Author

Alexander Adamchuk, May 10 2007

Keywords

• frac
• nonn

Comments

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

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. Cf. A100520 = Numerator of Sum_{k=0..2n} (-1)^k/C(2n, k)^2.

Programs

Mathematica

Table[ Numerator[ Sum[ (-1)^k / Binomial[2n,k]^3, {k,0,2n} ] ], {n,0,25} ]

Formula

a(n) = Numerator[ Sum[ (-1)^k / Binomial[2n,k]^3, {k,0,2n} ] ].