%I #17 Sep 08 2022 08:45:15
%S 0,3,10,35,1,30,1,291,253,378,1,782,1,2404,1260,291,1,3378,1,410,7899,
%T 3996,1,6030,126,10988,11188,5180,1,19712,1,8483,5334,34394,1841,
%U 21410,1,20580,39556,38810,1,64260,1,35972,66060,36504,1,61326,1716,123628
%N a(n) = C(2n-1,n-1) mod n^3.
%C For p prime > 3, Joseph Wolstenholme showed in 1862 that a(p)=1. - corrected by _Jonathan Sondow_, Jan 24 2016
%H Robert Israel, <a href="/A099907/b099907.txt">Table of n, a(n) for n = 1..10000</a>
%e a(11) = 352716 mod 1331 = 1.
%p seq(binomial(2*n-1,n-1) mod n^3, n=1..100); # _Robert Israel_, Jan 24 2016
%t Table[Mod[Binomial[2 n - 1, n - 1], n^3], {n, 1, 50}] (* _Vincenzo Librandi_, Jan 24 2016 *)
%o (PARI) a(n) = binomial(2*n-1, n-1) % n^3; \\ _Michel Marcus_, Jan 24 2016
%o (Magma) [Binomial(2*n-1, n-1) mod n^3: n in [1..50]]; // _Vincenzo Librandi_, Jan 24 2016
%Y Cf. A088218, A099905, A099906, A099908, A244214.
%K nonn
%O 1,2
%A _Henry Bottomley_, Oct 29 2004