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A053531
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E.g.f.: (1-x)^(-1/2*x)*exp(-1/2*x^2-1/4*x^3-1/8*x^4).
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1
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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; internal format)
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OFFSET
| 0,6
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COMMENTS
| The number of simple labelled graphs on n nodes whose connected components are wheels. - Geoffrey Critzer, Dec 10 2011
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REFERENCES
| R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.15(c).
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LINKS
| Vladimir Kruchinin, Compositae and their properties , arXiv:1103.2582
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FORMULA
| 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), n>0. [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 10 2010]
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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 *)
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PROG
| (Other) 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); (for Maxima) [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 10 2010]
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CROSSREFS
| Sequence in context: A145053 A168298 A126274 * A000476 A105451 A002603
Adjacent sequences: A053528 A053529 A053530 * A053532 A053533 A053534
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 16 2000
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