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A086677
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Number of Steiner topologies on n points.
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1
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1, 4, 31, 360, 5625, 110880, 2643795, 74035080, 2382538725, 86656878000, 3515761193175, 157425426358200, 7711961781949425, 410298436511964000, 23559634669682986875, 1452240056377167057000, 95649328231839993736125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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REFERENCES
| F. K. Hwang, D. S. Richards and P. Winter, The Steiner Tree Problem, North-Holland, 1992, see p. 14.
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FORMULA
| Let f(n) = (2*n-4)!/(2^(n-2)*(n-2)!) (A001147) and let F(n, k) = binomial(n, k+2) f(k) (n+k-2)! / (2k)!. Then a(n) = Sum_{k=0..n-2} Sum_{i=0..floor((n-k-2)/2)} binomial(n, i) F(n-i, k+i) (k+i)! / k!.
E.g.f.: 4*(x-3)/(x+1)^4 - (-13+22*x+3*x^2)/((-x^2-4*x+1)^(1/2)*(x+1)^4). - Mark van Hoeij, Oct 31 2011
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CROSSREFS
| Cf. A001147.
Sequence in context: A102757 A145561 A201628 * A016036 A000314 A128709
Adjacent sequences: A086674 A086675 A086676 * A086678 A086679 A086680
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jul 28 2003
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 29 2003
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