A099907 a(n) = C(2n-1,n-1) mod n^3.

0, 3, 10, 35, 1, 30, 1, 291, 253, 378, 1, 782, 1, 2404, 1260, 291, 1, 3378, 1, 410, 7899, 3996, 1, 6030, 126, 10988, 11188, 5180, 1, 19712, 1, 8483, 5334, 34394, 1841, 21410, 1, 20580, 39556, 38810, 1, 64260, 1, 35972, 66060, 36504, 1, 61326, 1716, 123628

Offset: 1

Author

Henry Bottomley, Oct 29 2004

Keywords

• nonn

Comments

For p prime > 3, Joseph Wolstenholme showed in 1862 that a(p)=1. - corrected by Jonathan Sondow, Jan 24 2016

Examples

			a(11) = 352716 mod 1331 = 1.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088218, A099905, A099906, A099908, A244214.

Programs

Magma

[Binomial(2*n-1, n-1) mod n^3: n in [1..50]]; // Vincenzo Librandi, Jan 24 2016

Maple

seq(binomial(2*n-1,n-1) mod n^3, n=1..100); # Robert Israel, Jan 24 2016

Mathematica

Table[Mod[Binomial[2 n - 1, n - 1], n^3], {n, 1, 50}] (* Vincenzo Librandi, Jan 24 2016 *)

PARI

a(n) = binomial(2*n-1, n-1) % n^3; \\ Michel Marcus, Jan 24 2016