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A032031
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Triple factorial numbers: (3n)!!!=3^n*n!.
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33
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1, 3, 18, 162, 1944, 29160, 524880, 11022480, 264539520, 7142567040, 214277011200, 7071141369600, 254561089305600, 9927882482918400, 416971064282572800, 18763697892715776000, 900657498850357248000
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OFFSET
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0,2
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COMMENTS
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For n >= 1 a(n) is the order of the wreath product of the symmetric group S_n and the elementary Abelian group (C_3)^n. - Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001
Laguerre transform of double factorials 2^n*n!=A000165(n). [From Paul Barry, Aug 08 2008]
For positive n, a(n) equals the permanent of the n X n matrix consisting entirely of 3's. [From John M. Campbell, May 26, 2011]
a(n) is the product of the positive integers <= 3*n that are multiples of 3. - Peter Luschny, Jun 23 2011
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REFERENCES
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Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..100
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 491
Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
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FORMULA
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a(n) = 3^n*n!.
a(n) = prod(k=1..n, 3*k ).
E.g.f.: 1/(1-3*x).
a(n)=sum{k=0..n, binomial(n,k)*(n!/k!)*2^k*k!}. [From Paul Barry, Aug 08 2008]
a(0) = 1, a(n) = 3*n*a(n-1). [Arkadiusz Wesolowski, Oct 04 2011]
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MAPLE
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with(combstruct):ZL:=[T, {T=Union(Z, Prod(Epsilon, Z, T), Prod(T, Z, Epsilon), Prod(T, Z))}, labeled]:seq(count(ZL, size=i)/i, i=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2007
A032031 := n -> mul(k, k = select(k-> k mod 3 = 0, [$1 .. 3*n])): seq(A032031(n), n = 0 .. 16);
- Peter Luschny, Jun 23 2011
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MATHEMATICA
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Table[3^n*Gamma[1 + n], {n, 0, 20}] - Roger L. Bagula, Oct 30 2008
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PROG
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(MAGMA) [3^n*Factorial(n): n in [0..60]]; // Vincenzo Librandi, Apr 22 2011
(PARI) a(n)=3^n*n!; /* or: */ a(n)=prod(k=1, n, 3*k );
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CROSSREFS
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Cf. A000142, A007559, A008544, A051141, A000165.
Sequence in context: A052182 A115415 A065058 * A127646 A089466 A107403
Adjacent sequences: A032028 A032029 A032030 * A032032 A032033 A032034
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Christian G. Bower
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STATUS
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approved
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