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A033678 Number of labeled Eulerian graphs with n nodes.
(Formerly M3146)
6
1, 0, 1, 3, 38, 720, 26614, 1858122, 250586792, 66121926720, 34442540326456, 35611003057733928, 73321307277341501168, 301201690357187097528960, 2471354321681605983102370864, 40525241311304939167532163726672 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

REFERENCES

F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 12, Eq. (1.4.6).

E. M. Palmer in L. W. Beineke and R. J. Wilson, Selected Topics in Graph Theory, Academic Press, NY, 1978, p. 385ff.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n=1..50

Huantian Cao, AutoGF: An Automated System to Calculate Coefficients of Generating Functions.

MAPLE

A033678 := proc(n) option remember; local k; if n=1 then 1 else 2^binomial(n-1, 2)-(1/n)*add(k*binomial(n, k)*2^binomial(n-k-1, 2)*A033678(k), k=1..n-1); fi; end;

MATHEMATICA

n = 16; (Series[ Log[ 1 + Sum[ 2^( (p-1)(p-2)/2 )x^p/(p!), {p, 1, n} ] ], {x, 0, n} ] // CoefficientList[#, x]& // Rest) * Range[n]! (* truncated exponential generating function *)

(* Second program: *)

a[n_] := a[n] = If[n == 1, 1, 2^Binomial[n-1, 2]-(1/n)*Sum[k*Binomial[n, k]*2^Binomial[n-k-1, 2]*a[k], {k, 1, n-1}]]; Table[a[n], {n, 1, 16}] (* Jean-Fran├žois Alcover, Feb 11 2014, after Maple *)

PROG

(Sage)

@cached_function

def A033678(n):

    if n == 1: return 1

    return 2^binomial(n-1, 2)-sum(k*2^((k-n+1)*(k-n+2)/2)*binomial(n, k)*A033678(k) for k in (1..n-1))/n

[A033678(n) for n in (1..16)] # Peter Luschny, Jan 17 2016

CROSSREFS

Sequence in context: A199025 A265914 A005780 * A228697 A072331 A109518

Adjacent sequences:  A033675 A033676 A033677 * A033679 A033680 A033681

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane, Geoffrey Mess (mess(AT)math.ucla.edu)

STATUS

approved

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Last modified November 14 08:13 EST 2018. Contains 317174 sequences. (Running on oeis4.)