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A133189 Number of simple directed graphs on n labeled nodes consisting only of some cycle graphs C_2 and nodes not part of a cycle having directed edges to both nodes in exactly one cycle. 4
1, 0, 1, 3, 9, 40, 210, 1176, 7273, 49932, 372060, 2971540, 25359411, 230364498, 2215550428, 22460391240, 239236043985, 2669869110856, 31134833803728, 378485082644400, 4786085290280275, 62838103267148790, 855122923978737876, 12042364529117844328 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..530

Eric Weisstein's World of Mathematics, Directed Graph

Eric Weisstein's World of Mathematics, Cycle Graph

FORMULA

a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k) * A006882(2*k-1) * k^(n-2*k).

E.g.f.: exp(exp(x)*x^2/2). - Geoffrey Critzer, Nov 23 2012

EXAMPLE

a(3) = 3, because there are 3 graphs of the given kind for 3 labeled nodes: 3->1<->2<-3,  2->1<->3<-2,  1->2<->3<-1.

MAPLE

a:= proc(n) option remember; add(binomial(n, k+k)*

      doublefactorial(k+k-1) *k^(n-k-k), k=0..floor(n/2))

    end:

seq(a(n), n=0..30);

# second Maple program:

a:= proc(n) option remember; `if`(n=0, 1, add(

      binomial(n-1, j-1) *binomial(j, 2) *a(n-j), j=1..n))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Mar 16 2015

MATHEMATICA

nn=20; Range[0, nn]!CoefficientList[Series[Exp[Exp[x]x^2/2], {x, 0, nn}], x]  (* Geoffrey Critzer, Nov 23 2012 *)

Table[Sum[BellY[n, k, Binomial[Range[n], 2]], {k, 0, n}], {n, 0, 25}] (* Vladimir Reshetnikov, Nov 09 2016 *)

CROSSREFS

Cf. A006882, A007318, A135458, A135429.

2th column of A145460, A143398.

Sequence in context: A229244 A218504 A292909 * A020092 A233533 A190341

Adjacent sequences:  A133186 A133187 A133188 * A133190 A133191 A133192

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 17 2007

STATUS

approved

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Last modified April 25 16:08 EDT 2019. Contains 322461 sequences. (Running on oeis4.)