A289278 a(n) = A005259(n) mod (2*n+1)^2.
0, 5, 23, 24, 34, 77, 22, 140, 50, 44, 169, 473, 354, 539, 198, 801, 385, 135, 1207, 617, 1483, 52, 2023, 528, 723, 2273, 2567, 1265, 1303, 2813, 550, 233, 1775, 188, 2365, 728, 154, 1520, 4180, 5585, 571, 236, 3650, 2672, 714, 4581, 4966, 2490, 8931, 4796, 1566
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
- Eric Weisstein's World of Mathematics, Apéry Number
Programs
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Mathematica
Table[Mod[Sum[(Binomial[n, k] Binomial[n + k, k])^2, {k, 0, n}], (2n + 1)^2], {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)^2; \\ Michel Marcus, Jul 01 2017
Formula
If m = 2*n + 1 is a prime, a(n) = A030211(n) mod m^2.