A202081 The number of simple labeled graphs on n nodes whose connected components are cycles, stars, wheels, or paths.

1, 1, 2, 8, 46, 298, 2206, 19009, 187076, 2053349, 24800484, 327067043, 4677505768, 72075818159, 1189985755128, 20952274850927, 391829421176768, 7755079821666945, 161926610838369418, 3556807008080385549, 81979632030102053376, 1978135038931568355707

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