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A108246 Number of labeled 2-regular graphs with no multiple edges, but loops are allowed (i.e., each vertex is endpoint of two (usual) edges or one loop). 3
1, 1, 1, 2, 8, 38, 208, 1348, 10126, 86174, 819134, 8604404, 98981944, 1237575268, 16710431992, 242337783032, 3756693451772, 61991635990652, 1084943597643964, 20072853005524696, 391443701509660096, 8024999955144721256, 172544980412641191776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

Linear recurrence satisfied by a(n): {a(2) = 1, a(0) = 1, (-n^2 - 3*n - 2)*a(n) + (4 + 2*n)*a(n+1) + (-2*n-6)*a(n+2) + 2*a(n+3), a(1) = 1}.

E.g.f.: exp(-t^2/4 + t/2)/sqrt(1-t). - Vladeta Jovovic, Aug 14 2006

a(n) ~ sqrt(2)*n^n/exp(n-1/4). - Vaclav Kotesovec, Oct 17 2012

EXAMPLE

a(3) = 2: {(1,2) (2,3) (1,3)}, {(1,1) (2,2) (3,3)}.

MAPLE

b:= proc(n) option remember; if n=0 then 1 elif n<3 then 0 else (n-1) *(b(n-1) +b(n-3) *(n-2)/2) fi end: a:= proc(n) add(b(k) *binomial(n, k), k=0..n) end: seq(a(n), n=0..30);  # Alois P. Heinz, Sep 12 2008

MATHEMATICA

CoefficientList[Series[E^(-x^2/4+x/2)/Sqrt[1-x], {x, 0, 20}], x]* Table[n!, {n, 0, 20}] (* Vaclav Kotesovec, Oct 17 2012 *)

CROSSREFS

Cf. A000985, A002137.

Binomial transform of A001205.

Row sums of A144161. - Alois P. Heinz, Jun 01 2009

Sequence in context: A266797 A234939 A192784 * A020031 A179323 A001340

Adjacent sequences:  A108243 A108244 A108245 * A108247 A108248 A108249

KEYWORD

nonn

AUTHOR

Marni Mishna, Jun 17 2005

EXTENSIONS

More terms from Alois P. Heinz, Sep 12 2008

STATUS

approved

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Last modified May 24 15:25 EDT 2019. Contains 323532 sequences. (Running on oeis4.)