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A065961
a(n) = (3*n - 1)!*n/2.
2
1, 120, 60480, 79833600, 217945728000, 1067062284288000, 8515157028618240000, 103408066955539906560000, 1814811575069725360128000000, 44208809968698509772718080000000, 1447219603135314415919699066880000000, 61998887798316869577999908025139200000000
OFFSET
1,2
LINKS
FORMULA
a(n) = (3*n)! / 6.
a(n) - 3*n*(3*n-1)*(3*n-2)*a(n-1) = 0. - R. J. Mathar, Oct 31 2015
From Amiram Eldar, Feb 17 2024: (Start)
Sum_{n>=1} 1/a(n) = 2*e - 6 + 4*cos(sqrt(3)/2)/sqrt(e).
Sum_{n>=1} (-1)^(n+1)/a(n) = 6 - 2/e - 4*sqrt(e)*cos(sqrt(3)/2). (End)
MATHEMATICA
(3*Range[15])!/6 (* Paolo Xausa, Feb 16 2024 *)
PROG
(PARI) { for (n=1, 60, a=(3*n - 1)!*n/2; write("b065961.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 04 2009
(Magma) [ Factorial(3*n)/6: n in [1..62] ]; // Vincenzo Librandi, Apr 24 2011
CROSSREFS
Cf. A100732.
Sequence in context: A109897 A301393 A074653 * A364512 A333043 A058528
KEYWORD
nonn
AUTHOR
STATUS
approved