%I A010763
%S A010763 0,2,9,34,125,461,1715,6434,24309,92377,352715,1352077,5200299,
%T A010763 20058299,77558759,300540194,1166803109,4537567649,17672631899,
%U A010763 68923264409,269128937219,1052049481859,4116715363799,16123801841549
%N A010763 C(2n+1,n+1)-1.
%C A010763 (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
%H A010763 Eric Weisstein, The World of Mathematics: <a href="http://mathworld.wolfram.com/
               WolstenholmesTheorem.html">Wolstenholme's Theorem</a>.
%F A010763 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
%F A010763 a(n)=sum(i=1, n, C(n+i, n)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Oct 15 2002
%Y A010763 A001700-1.
%Y A010763 Cf. A001008, A007406, A112861, A112862, A034602.
%Y A010763 Sequence in context: A109719 A000524 A120989 this_sequence A077234 A091526 
               A150937
%Y A010763 Adjacent sequences: A010760 A010761 A010762 this_sequence A010764 A010765 
               A010766
%K A010763 nonn,easy
%O A010763 0,2
%A A010763 N. J. A. Sloane (njas(AT)research.att.com).