A099906 a(n) = binomial(2n-1,n-1) mod n^2.

0, 3, 1, 3, 1, 30, 1, 35, 10, 78, 1, 62, 1, 52, 135, 35, 1, 138, 1, 10, 402, 124, 1, 270, 126, 172, 253, 476, 1, 812, 1, 291, 978, 870, 616, 674, 1, 364, 10, 410, 1, 756, 1, 1124, 1260, 532, 1, 1422, 1716, 1128, 2322, 1556, 1, 1920, 1941, 2172, 1815, 844, 1, 3528, 1, 964

Offset

1,2

Comments

For odd primes p, Charles Babbage showed in 1819 that a(p) = 1.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

a(11) = binomial(21,10) mod 11^2 = 352716 mod 121 = 1.

Mathematica

Table[ Mod[ Binomial[2n - 1, n - 1], n^2], {n, 60}] (* Robert G. Wilson v, Dec 14 2004 *)

Prog

(Magma) [Binomial(2*n-1, n-1) mod(n^2): n in [1..65]]; // Vincenzo Librandi, Jul 29 2015
(PARI) A099906(n)=binomial(2*n-1, n-1)%n^2 \\ M. F. Hasler, Jul 30 2015
(Python)
from __future__ import division
A099906_list, b = [], 1
for n in range(1, 10001):
    A099906_list.append(b % n**2)
    b = b*2*(2*n+1)//(n+1) # Chai Wah Wu, Jan 26 2016

Crossrefs

Cf. A088218, A099905, A099907, A099908.

Sequence in context: A278601 A281038 A263677 * A262026 A270390 A341472

Adjacent sequences: A099903 A099904 A099905 * A099907 A099908 A099909

Keyword

nonn

Author

Henry Bottomley, Oct 29 2004

Status

approved