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A100732 a(n) = (3*n)!. 10
1, 6, 720, 362880, 479001600, 1307674368000, 6402373705728000, 51090942171709440000, 620448401733239439360000, 10888869450418352160768000000, 265252859812191058636308480000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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 subdiagonal, and 1's everywhere else (see Mathematica code below). - John M. Campbell, Jul 12 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

FORMULA

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

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}] (* John M. Campbell, Jul 12 2011 *)

(3Range[0, 10])! (* Harvey P. Dale, Sep 23 2011 *)

PROG

(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

CROSSREFS

Cf. A000142, A010050, A100733, A100734, A143819, A268504.

Sequence in context: A014525 A289747 A188960 * A003923 A002204 A052295

Adjacent sequences:  A100729 A100730 A100731 * A100733 A100734 A100735

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Dec 08 2004

STATUS

approved

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Last modified August 12 08:40 EDT 2022. Contains 356067 sequences. (Running on oeis4.)