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
Keywords
Examples
a(11) = binomial(21,10) mod 11^2 = 352716 mod 121 = 1.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
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Magma
[Binomial(2*n-1, n-1) mod(n^2): n in [1..65]]; // Vincenzo Librandi, Jul 29 2015
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Mathematica
Table[ Mod[ Binomial[2n - 1, n - 1], n^2], {n, 60}] (* Robert G. Wilson v, Dec 14 2004 *) -
PARI
A099906(n)=binomial(2*n-1,n-1)%n^2 \\ M. F. Hasler, Jul 30 2015
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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
Comments