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

1,2

Comments

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

Links

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

Example

a(11) = 352716 mod 1331 = 1.

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 *)

Prog

(PARI) a(n) = binomial(2*n-1, n-1) % n^3; \\ Michel Marcus, Jan 24 2016
(Magma) [Binomial(2*n-1, n-1) mod n^3: n in [1..50]]; // Vincenzo Librandi, Jan 24 2016

Crossrefs

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

Sequence in context: A149033 A149034 A149035 * A128735 A330050 A159309

Adjacent sequences: A099904 A099905 A099906 * A099908 A099909 A099910

Keyword

nonn

Author

Henry Bottomley, Oct 29 2004

Status

approved