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%I #20 Mar 30 2017 09:00:12
%S 1,1,10,220,7315,324632,18009460,1198774720,93080887185,8258898672310,
%T 824313388697656,91408035226209520,11149106984707682900,
%U 1483408105790477598270,213807915740948618992925,33186033477308745271085760,5518696446064784220490766525
%N a(n) = binomial(n*(3*n-1)/2, n).
%H G. C. Greubel, <a href="/A199748/b199748.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) = binomial(A000326(n), n), where A000326 are pentagonal numbers.
%F a(n) is divisible by 5 for gcd(n,5) = 1 and n>0.
%F a(n) ~ n^(n-1/2) * exp(n-2/3) * 3^n / (sqrt(Pi) * 2^(n+1/2)). - _Vaclav Kotesovec_, Apr 23 2015
%e a(2) = C(5,2) = 10; a(3) = C(12,3) = 220; a(4) = C(22,4) = 7315; a(5) = C(35,5) = 324632; ...
%t Table[Binomial[n*(3n-1)/2,n],{n,0,20}] (* _Harvey P. Dale_, Aug 16 2012 *)
%o (PARI) {a(n)=binomial(n*(3*n-1)/2,n)}
%Y Cf. A199747, A000326, A001318.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 09 2011
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