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A089461 Hyperbinomial transform of A088957. Also the row sums of triangle A089460, which lists the coefficients for the second hyperbinomial transform. 4
1, 3, 13, 81, 689, 7553, 101961, 1639529, 30640257, 653150529, 15649353929, 416495026841, 12193949444193, 389572905351425, 13488730646528265, 503205102139969977, 20123584054543823105, 858863606297804378753, 38967500492977755457161, 1872974608860684814735385 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

FORMULA

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.

a(n) ~ 2*exp(2+exp(-1))*n^(n-1). - Vaclav Kotesovec, Jul 08 2013

MAPLE

a:= n-> add(2*(n-j+2)^(n-j-1)*binomial(n, j), j=0..n):

seq (a(n), n=0..20);  # Alois P. Heinz, Oct 30 2012

MATHEMATICA

CoefficientList[Series[E^x*(-LambertW[-x]/x)^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jul 08 2013 *)

PROG

(PARI) x='x+O('x^50); Vec(serlaplace(exp(x)*(-lambertw(-x)/x)^2)) \\ G. C. Greubel, Nov 16 2017

CROSSREFS

Cf. A088957, A089460 (triangle).

Column k=2 of A144303. - Alois P. Heinz, Oct 30 2012

Sequence in context: A135921 A005923 A335588 * A000684 A222272 A057993

Adjacent sequences:  A089458 A089459 A089460 * A089462 A089463 A089464

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 05 2003

STATUS

approved

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Last modified June 12 20:20 EDT 2021. Contains 344964 sequences. (Running on oeis4.)