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A000846 C(3n,n) - C(2n,n). 3
0, 1, 9, 64, 425, 2751, 17640, 112848, 722601, 4638205, 29860259, 192831288, 1248973544, 8112024844, 52820112480, 344712308064, 2254247833257, 14768735480505, 96917273443305, 636948624057900, 4191706659276675, 27618897144488595, 182181063882796680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

T. D. Noe, Table of n, a(n) for n = 0..200

FORMULA

a(n) = sum(k = 1..n, binomial(n,k)*binomial(2*n,n-k)). - Vladimir Kruchinin, Nov 12 2014

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

MAPLE

seq(binomial(3*n, n)-binomial(2*n, n), n=0..10) ; # R. J. Mathar, May 05 2018

MATHEMATICA

Table[Binomial[3*n, n] - Binomial[2*n, n], {n, 0, 20}] (* T. D. Noe, Jun 20 2012 *)

PROG

(MAGMA) [Binomial(3*n, n)-Binomial(2*n, n): n in [0..30]]; // Vincenzo Librandi, Nov 12 2014

CROSSREFS

Sequence in context: A000444 A143631 A083328 * A231822 A049684 A037540

Adjacent sequences:  A000843 A000844 A000845 * A000847 A000848 A000849

KEYWORD

nonn,easy

AUTHOR

Brendan McKay

STATUS

approved

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Last modified August 19 01:39 EDT 2018. Contains 313840 sequences. (Running on oeis4.)