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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: A079412 A262940 A263677 * A262026 A270390 A047787

Adjacent sequences:  A099903 A099904 A099905 * A099907 A099908 A099909

KEYWORD

nonn

AUTHOR

Henry Bottomley, Oct 29 2004

STATUS

approved

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Last modified May 31 23:19 EDT 2016. Contains 273548 sequences.