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1, 6, 720, 362880, 479001600, 1307674368000, 6402373705728000, 51090942171709440000, 620448401733239439360000, 10888869450418352160768000000, 265252859812191058636308480000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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 the subdiagonal, and 1's everywhere else (see Mathematica code below). [From John M. Campbell, Jul 12 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
| E.g.f.: 1/(1-x^3).
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MATHEMATICA
| 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}] (* From John M. Campbell, Jul 12 2011 *)
(3Range[0, 10])! (* From Harvey P. Dale, Sep 23 2011 *)
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PROG
| (Other) sage: [stirling_number1(3*n+1, 1) for n in xrange(0, 11)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 26 2009]
(MAGMA) [Factorial(3*n): n in [0..15]]; // Vincenzo Librandi, Sep 24 2011
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CROSSREFS
| Cf. A000142, A010050, A100733, A100734.
Sequence in context: A201391 A014525 A188960 * A003923 A002204 A052295
Adjacent sequences: A100729 A100730 A100731 * A100733 A100734 A100735
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KEYWORD
| nonn,easy
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AUTHOR
| Ralf Stephan, Dec 08 2004
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