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A053531 E.g.f.: (1-x)^(-1/2*x)*exp(-1/2*x^2-1/4*x^3-1/8*x^4). 1
1, 0, 0, 0, 1, 15, 72, 420, 2915, 24570, 245070, 2633400, 30588783, 383841315, 5197243590, 75666140550, 1177491151785, 19496256883740, 342184849138188, 6346249258076280, 124023565540658025, 2547445128977720475, 54865546632888272820 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

The number of simple labeled graphs on n nodes whose connected components are wheels. - Geoffrey Critzer, Dec 10 2011

REFERENCES

R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.15(c).

LINKS

Table of n, a(n) for n=0..22.

Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582

FORMULA

a(n) = n!*sum((-2)^(-m)/m!*sum(C(m,k)*sum(2^(k-i)*sum(C(k,j)*C(j,i-3*k+2*j), j=0..k)*(-1)^(n-m-i-2*(m-k))*(m-k)!/(n-m-i)!*stirling1(n-m-i,m-k), i=k..n-2*m+k), k=0..m), m=1..n), n>0. - Vladimir Kruchinin, Sep 10 2010

MATHEMATICA

nn = 16; a = Sum[(n (n - 2)!/2) x^n/n!, {n, 5, nn}]; Range[0, nn]! CoefficientList[Series[Exp[x^4/4! + a], {x, 0, nn}], x]  (* Geoffrey Critzer, Dec 10 2011 *)

PROG

(Maxima) a(n):=n!*sum((-2)^(-m)/m!*sum(binomial(m, k)*sum(2^(k-i)* sum(binomial(k, j)*binomial(j, i-3*k+2*j), j, 0, k)*(-1)^(n-m-i-2*(m-k))*(m-k)!/(n-m-i)!*stirling1(n-m-i, m-k), i, k, n-2*m+k), k, 0, m), m, 1, n); [Vladimir Kruchinin, Sep 10 2010]

CROSSREFS

Sequence in context: A241234 A212097 A212098 * A000476 A002603 A212562

Adjacent sequences:  A053528 A053529 A053530 * A053532 A053533 A053534

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 16 2000

STATUS

approved

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Last modified November 20 09:08 EST 2018. Contains 317385 sequences. (Running on oeis4.)