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%I #26 Feb 17 2024 04:03:32
%S 1,120,60480,79833600,217945728000,1067062284288000,
%T 8515157028618240000,103408066955539906560000,
%U 1814811575069725360128000000,44208809968698509772718080000000,1447219603135314415919699066880000000,61998887798316869577999908025139200000000
%N a(n) = (3*n - 1)!*n/2.
%H Harry J. Smith, <a href="/A065961/b065961.txt">Table of n, a(n) for n = 1..60</a>
%F a(n) = (3*n)! / 6.
%F a(n) - 3*n*(3*n-1)*(3*n-2)*a(n-1) = 0. - _R. J. Mathar_, Oct 31 2015
%F From _Amiram Eldar_, Feb 17 2024: (Start)
%F Sum_{n>=1} 1/a(n) = 2*e - 6 + 4*cos(sqrt(3)/2)/sqrt(e).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 6 - 2/e - 4*sqrt(e)*cos(sqrt(3)/2). (End)
%t (3*Range[15])!/6 (* _Paolo Xausa_, Feb 16 2024 *)
%o (PARI) { for (n=1, 60, a=(3*n - 1)!*n/2; write("b065961.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 04 2009
%o (Magma) [ Factorial(3*n)/6: n in [1..62] ]; // _Vincenzo Librandi_, Apr 24 2011
%Y Cf. A100732.
%K nonn
%O 1,2
%A _Len Smiley_ and _George E. Antoniou_, Dec 08 2001