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A100732
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a(n) = (3*n)!.
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10
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1, 6, 720, 362880, 479001600, 1307674368000, 6402373705728000, 51090942171709440000, 620448401733239439360000, 10888869450418352160768000000, 265252859812191058636308480000000
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OFFSET
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0,2
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COMMENTS
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a(n) equals (-1)^n times the determinant of the (3n+1) X (3n+1) matrix with consecutive integers from 1 to 3n+1 along the main diagonal, consecutive integers from 2 to 3n+1 along the superdiagonal, consecutive integers from 1 to 3n along the subdiagonal, and 1's everywhere else (see Mathematica code below). - John M. Campbell, Jul 12 2011
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
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a(n) = A000142(A008585(n)).
E.g.f.: 1/(1-x^3).
From Ilya Gutkovskiy, Jan 20 2017: (Start)
a(n) ~ sqrt(2*Pi)*3^(3*n+1/2)*n^(3*n+1/2)/exp(3*n).
Sum_{n>=0} 1/a(n) = (exp(3/2) + 2*cos(sqrt(3)/2))/(3*exp(1/2)) = A143819. (End)
Sum_{n>=0} (-1)^n/a(n) = (1 + 2*exp(3/2)*cos(sqrt(3)/2))/(3*e). - Amiram Eldar, Feb 14 2021
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MATHEMATICA
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Table[(-1)^n*Det[Array[KroneckerDelta[#1, #2]*(#1 - 1) + KroneckerDelta[#1, #2 - 1]*(#1) + KroneckerDelta[#1, #2 + 1]*(#1 - 2) + 1 &, {3*n + 1, 3*n + 1}]], {n, 0, 24}] (* John M. Campbell, Jul 12 2011 *)
(3Range[0, 10])! (* Harvey P. Dale, Sep 23 2011 *)
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PROG
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(Sage)
[factorial(3*n) for n in range(0, 11)] # Peter Luschny, Jun 06 2016
(MAGMA)
[Factorial(3*n): n in [0..15]]; // Vincenzo Librandi, Sep 24 2011
(Haskell)
a100732 = a000142 . a008585 -- Reinhard Zumkeller, Feb 19 2013
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CROSSREFS
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Cf. A000142, A010050, A100733, A100734, A143819, A268504.
Sequence in context: A014525 A289747 A188960 * A003923 A002204 A052295
Adjacent sequences: A100729 A100730 A100731 * A100733 A100734 A100735
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KEYWORD
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nonn,easy
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AUTHOR
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Ralf Stephan, Dec 08 2004
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STATUS
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approved
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