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A202081 The number of simple labeled graphs on n nodes whose connected components are cycles, stars, wheels, or paths. 1
1, 1, 2, 8, 46, 298, 2206, 19009, 187076, 2053349, 24800484, 327067043, 4677505768, 72075818159, 1189985755128, 20952274850927, 391829421176768, 7755079821666945, 161926610838369418, 3556807008080385549, 81979632030102053376, 1978135038931568355707 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Here a cycle is of length 3 or more, a star has at least 4 (total) vertices, a wheel has at least 4 (total) vertices, and a path can be an isolated vertex.

REFERENCES

R. P. Stanley, Enumerative Combinatorics Volume 2, Cambridge 1999, problem 5.15

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..440

FORMULA

E.g.f.: exp(x/2+x/(2(1-x))*exp(-x^2/2-x^3/4-x^4/8)/(1-x)^(x/2)* exp(-x-x^2/2-x^3/2 + x exp(x))*exp(-x/2-x^2/4)/(1-x)^(1/2).

MATHEMATICA

nn = 16; a = x/(2 (1 - x)) + x/2; b = x^4/4! + Sum[(n (n - 2)!/2) x^n/n!, {n, 5, nn}]; c = x Exp[x] - x^3/2 - x^2 - x; d = -x/2 - x^2/4; Range[0, nn]! CoefficientList[Series[Exp[a]*Exp[b]*Exp[c]*Exp[d]/(1 - x)^(1/2), {x, 0, nn}], x]

CROSSREFS

Cf. A001205, A053530, A053531, A011800.

Sequence in context: A183277 A269006 A266507 * A258315 A334498 A006664

Adjacent sequences:  A202078 A202079 A202080 * A202082 A202083 A202084

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Dec 10 2011

STATUS

approved

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Last modified June 28 21:04 EDT 2022. Contains 354907 sequences. (Running on oeis4.)