A289277 a(n) = A005259(n) mod 2*n+1.

0, 2, 3, 3, 7, 0, 9, 5, 16, 6, 1, 13, 4, 26, 24, 26, 22, 30, 23, 32, 7, 9, 43, 11, 37, 29, 23, 0, 49, 40, 1, 44, 20, 54, 19, 18, 8, 20, 22, 55, 4, 70, 80, 62, 2, 31, 37, 20, 7, 44, 51, 62, 64, 76, 77, 41, 75, 75, 115, 68, 0, 35, 42, 11, 88, 59, 101, 35, 119, 11

Offset: 0

Author

Seiichi Manyama, Jul 01 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• F. Beukers, Another congruence for the Apéry numbers, J. Number Theory 25 (1987), no. 2, 201-210.
• Eric Weisstein's World of Mathematics, Apéry Number

Crossrefs

Cf. A005259, A030211, A289278.

Programs

Mathematica

Table[Mod[Sum[(Binomial[n, k] Binomial[n + k, k])^2, {k, 0, n}], 2n + 1], {n, 0, 100}] (* Indranil Ghosh, Jul 01 2017 *)

PARI

a(n) = sum(k=0, n, (binomial(n, k)*binomial(n+k, k))^2) % (2*n+1); \\ Michel Marcus, Jul 01 2017

Formula

If m = 2*n + 1 is a prime, a(n) = A030211(n) mod m.