A071405 (1/2)*((Sum_{k=0..p} C(p,k)*C(p+k,k)) - 2^p - 1)/p^2 where p runs through the primes.

1, 3, 33, 495, 186135, 4171377, 2466841857, 63503364807, 45502121922063, 1000280542916542065, 28769246281107682239, 725108164366019776175793, 647570641899231298169462337, 19531524543125261885413183191, 18049654140244780945166233169055, 524148959609231196591306213067941297

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..214

Mathematica

Table[(LegendreP[p, 3] - 2^p - 1)/(2*p^2), {p, Prime[Range[16]]}] (* Amiram Eldar, Apr 26 2025 *)

Prog

(PARI) a(n) = {my(p=prime(n)); (1/2)*(sum(k=0, p, binomial(p, k)*binomial(p+k, k)) - 2^p - 1)/p^2} \\ Jason Yuen, Jan 09 2025

Crossrefs

Cf. A001850.

Sequence in context: A365028 A368442 A264833 * A234526 A243251 A336539

Adjacent sequences: A071402 A071403 A071404 * A071406 A071407 A071408

Keyword

nonn

Author

Benoit Cloitre, Feb 13 2003

Status

approved