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A011781 Sextuple factorial numbers: product[ k=0..n-1 ] (6*k+3). 9
1, 3, 27, 405, 8505, 229635, 7577955, 295540245, 13299311025, 678264862275, 38661097149675, 2435649120429525, 168059789309637225, 12604484198222791875, 1020963220056046141875, 88823800144876014343125 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Total number of Eulerian circuits in rooted labeled multigraphs with n edges. - Valery A. Liskovets, Apr 07 2002

REFERENCES

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.

LINKS

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

FORMULA

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]

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A001147, A047657, A049308.

Cf. A069736.

Sequence in context: A138436 A141057 A201696 * A094577 A221624 A108525

Adjacent sequences:  A011778 A011779 A011780 * A011782 A011783 A011784

KEYWORD

nonn

AUTHOR

killough(AT)wagner.convex.com (Lee D. Killough)

STATUS

approved

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Last modified May 20 15:40 EDT 2013. Contains 225463 sequences.