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A000846
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a(n) = C(3n,n) - C(2n,n).
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3
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0, 1, 9, 64, 425, 2751, 17640, 112848, 722601, 4638205, 29860259, 192831288, 1248973544, 8112024844, 52820112480, 344712308064, 2254247833257, 14768735480505, 96917273443305, 636948624057900, 4191706659276675, 27618897144488595, 182181063882796680
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OFFSET
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0,3
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COMMENTS
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It appears that, with the exception of n = 49, a(n)== 1 (mod n^2) only if n is prime. (Tested to 10,000.) - Gary Detlefs, Aug 06 2013
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LINKS
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FORMULA
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2*n*(n-1)*(2*n-1)*(11*n^2-33*n+24)*a(n) -(n-1) *(473*n^4 -1892*n^3 +2561*n^2 -1338*n +216) *a(n-1) +6 *(3*n-5) *(3*n-4) *(2*n-3) *(11*n^2-11*n+2) *a(n-2)=0. - R. J. Mathar, May 05 2018
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MAPLE
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seq(binomial(3*n, n)-binomial(2*n, n), n=0..10) ; # R. J. Mathar, May 05 2018
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MATHEMATICA
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Table[Binomial[3*n, n] - Binomial[2*n, n], {n, 0, 20}] (* T. D. Noe, Jun 20 2012 *)
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PROG
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(Magma) [Binomial(3*n, n)-Binomial(2*n, n): n in [0..30]]; // Vincenzo Librandi, Nov 12 2014
(Python)
from math import comb
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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