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A011781
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Sextuple factorial numbers: product[ k=0..n-1 ] (6*k+3).
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9
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1, 3, 27, 405, 8505, 229635, 7577955, 295540245, 13299311025, 678264862275, 38661097149675, 2435649120429525, 168059789309637225, 12604484198222791875, 1020963220056046141875, 88823800144876014343125
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OFFSET
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0,2
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COMMENTS
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Total number of Eulerian circuits in rooted labeled multigraphs with n edges. - Valery A. Liskovets, Apr 07 2002
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REFERENCES
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V. A. Liskovets, A note on the total number of Eulerian circuits in multigraphs. In press.
B.Lass, D'emonstration combinatoire de la formule de Harer-Zagier, C. R. Acad. Sci. Paris, Serie I, 333 (2001) No 3, 155-160.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Valery Liskovets, A Note on the Total Number of Double Eulerian Circuits in Multigraphs , Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.5
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FORMULA
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E.g.f. (1-6*x)^(-1/2).
a(n) = 3^n*(2*n-1)!!.
G.f.: 1/(1-3x/(1-6x/(1-9x/(1-12x/(1-15x/(1-18x/(1-21x/(1-24x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012
a(n)=(-3)^n*sum_{k=0..n} 2^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. [From Mircea Merca, May 03 2012]
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MATHEMATICA
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s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 2, 5!, 6}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 08 2008]
Table[Product[6k+3, {k, 0, n-1}], {n, 0, 20}] (* or *) Table[6^(n-1) Pochhammer[ 1/2, n-1], {n, 21}] (* From Harvey P. Dale, May 09 2012 *)
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PROG
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(PARI) a(n)=if(n<0, 0, (3/2)^n*(2*n)!/n!)
(MAGMA) [(3/2)^n*Factorial(2*n)/Factorial(n):n in [0..20]]; // Vincenzo Librandi, May 09 2012
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CROSSREFS
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Cf. A001147, A047657, A049308.
Cf. A069736.
Sequence in context: A138436 A141057 A201696 * A094577 A221624 A108525
Adjacent sequences: A011778 A011779 A011780 * A011782 A011783 A011784
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KEYWORD
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nonn
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AUTHOR
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killough(AT)wagner.convex.com (Lee D. Killough)
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STATUS
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approved
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