login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A099906 a(n) = binomial(2n-1,n-1) mod n^2. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A262940 A278601 A263677 * A262026 A270390 A047787

Adjacent sequences:  A099903 A099904 A099905 * A099907 A099908 A099909

KEYWORD

nonn

AUTHOR

Henry Bottomley, Oct 29 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 3 16:24 EST 2016. Contains 278745 sequences.