login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A069736 Total number of Eulerian circuits in labeled multigraphs with n edges. 1
1, 2, 13, 150, 2541, 57330, 1623105, 55405350, 2216439225, 101738006370, 5271938032725, 304455567165750, 19391501988260325, 1350480167457671250, 102096314890336391625, 8327231070135771543750, 728877648485930118800625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

B. Lass, Démonstration combinatoire de la formule de Harer-Zagier, (A combinatorial proof of the Harer-Zagier formula) C. R. Acad. Sci. Paris, Serie I, 333 (2001) No 3, 155-160.

B. Lass, Démonstration combinatoire de la formule de Harer-Zagier, (A combinatorial proof of the Harer-Zagier formula) C. R. Acad. Sci. Paris, Serie I, 333 (2001) No 3, 155-160.

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

a(n) = (2*n)!/(2^n*n!)(3^(n+1)-1)/(2*(n+1)).

E.g.f.: (sqrt(1-2*x)-sqrt(1-6*x))/(2*x).

From Sergei N. Gladkovskii, Jul 25 2012 (Start)

G.f. 1 + 8*x/(G(0)-8*x); where G(k)= x*(k+1)*(2*k+1)*(9*3^k-1) + (k+2)*(3*3^k-1) - x*((k+2)^2)*(3*3^k-1)*(2*k+3)*(27*3^k-1)/G(k+1);(continued fraction, Euler's 1st kind, 1-step).

G.f. 3/2*G(0) where G(k)= 1 - 1/(3*3^k - 27*x*(k+1)*(2*k+1)*9^k/(9*x*(2*k+1)*(k+1)*3^k - (k+2)/Q2)); (continued fraction, 3rd kind, 3-step).

E.g.f. (sqrt(1-2*x)-sqrt(1-6*x))/(2*x)= G(0)/(2*x); where G(k)= 1 - 3^k/(1 - x*(2*k-1)/(x*(2*k-1) - 3^k*(k+1)/G(k+1))); (continued fraction, 3rd kind, 3-step).

(End)

PROG

(PARI) x=xx+O(xx^33); Vec(serlaplace((sqrt(1-2*x)-sqrt(1-6*x))/(2*x))) \\ Michel Marcus, Dec 11 2014

CROSSREFS

Cf. A011781.

Sequence in context: A079330 A059367 A204554 * A058192 A054382 A062593

Adjacent sequences:  A069733 A069734 A069735 * A069737 A069738 A069739

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Apr 07 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 21 12:51 EST 2017. Contains 295001 sequences.