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A089461
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Hyperbinomial transform of A088957. Also the row sums of triangle A089460, which lists the coefficients for the second hyperbinomial transform.
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5
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1, 3, 13, 81, 689, 7553, 101961, 1639529, 30640257, 653150529, 15649353929, 416495026841, 12193949444193, 389572905351425, 13488730646528265, 503205102139969977, 20123584054543823105, 858863606297804378753, 38967500492977755457161, 1872974608860684814735385
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OFFSET
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0,2
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COMMENTS
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a(n) is also the number of subtrees of the complete graph K_{n+1} which contain a fixed edge. For n=2, the a(2)=3 solutions are the 3 subtrees of complete graph K_3 which contain a fixed edge (i.e. the edge itself and 2 copies of K_{1,2}). - Kellie J. MacPhee, Jul 25 2013
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} 2*(n-k+2)^(n-k-1)*C(n, k).
E.g.f.: exp(x)*(-LambertW(-x)/x)^2.
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MAPLE
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a:= n-> add(2*(n-j+2)^(n-j-1)*binomial(n, j), j=0..n):
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MATHEMATICA
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CoefficientList[Series[E^x*(-LambertW[-x]/x)^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jul 08 2013 *)
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PROG
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(PARI) x='x+O('x^50); Vec(serlaplace(exp(x)*(-lambertw(-x)/x)^2)) \\ G. C. Greubel, Nov 16 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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