0,2

(With a different offset:) p divides a(p) for prime p. p^2 divides a(p) for prime p>2. p^3 divides a(p) for prime p>3 (implied by the Wolstenholme's Theorem). Wolstenholme's quotients ale listed in A034602(n) = a(Prime(n))/Prime(n)^3 = {1, 5, 265, 2367, 237493, 2576561, 338350897, ...} = a(p)/p^3 for prime p>3. p^3 divides a(p^k) for prime p>3 and integer k>0. Primes in a(n) are listed in A112862(n) = {2, 461, 92377, 269128937219, ...} Primes of the form (2*n)!/(2*(n!)^2)-1. Numbers n such that a(n) is prime are listed in A112861(n) = {2, 6, 10, 21, 45, 63, 306, 404, 437, 471, 646, ...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 05 2007

Eric Weisstein, The World of Mathematics: Wolstenholme's Theorem.

a(n)=(n/(2n+2))*sum(k=1, n+1, C(2n+2, k)/C(n+1, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 20 2002

a(n)=sum(i=1, n, C(n+i, n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 15 2002

A001700-1.

Cf. A001008, A007406, A112861, A112862, A034602.

Sequence in context: A109719 A000524 A120989 this_sequence A077234 A091526 A150937

Adjacent sequences: A010760 A010761 A010762 this_sequence A010764 A010765 A010766

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).