A320624 a(n) = (A006134((prime(n)-1)/2) - Legendre(prime(n), 3))/prime(n).

1, 2, 4, 32, 98, 1034, 3484, 41582, 1868198, 6751460, 330246410, 4522217312, 16829506610, 235344648416, 12559206444236, 683534482499900, 2599887148071402, 144419015585768252, 2117118216002111198, 8120930597438173620

Offset

2,2

Comments

a(n) is always an integer.

Primes p such that p^2 divides A006134((p-1)/2) - Legendre(p, 3) are p = 103, ... What's the next?

Links

Table of n, a(n) for n=2..21.

Formula

a(2) = (binomial(0, 0) + binomial(2, 1))/3 = 3/3 = 1.

a(3) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + 1)/5 = 10/5 = 2.

a(4) = (binomial(0, 0) + binomial(2, 1) + binomial(4, 2) + binomial(6, 3) - 1)/7 = 28/7 = 4.

Prog

(PARI) A006134(n) = sum(k=0, n, binomial(2*k, k))
a(n) = my(p=prime(n)); (A006134((p-1)/2) - kronecker(p, 3))/p

Crossrefs

Cf. A006134, A102283, A320626.

Sequence in context: A197099 A009098 A192387 * A133127 A122693 A019060

Adjacent sequences: A320621 A320622 A320623 * A320625 A320626 A320627

Keyword

nonn

Author

Jianing Song, Oct 18 2018

Status

approved