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A089464 Hyperbinomial transform of A089461. Also the row sums of triangle A089463, which lists the coefficients for the third hyperbinomial transform. 4
1, 4, 22, 163, 1564, 18679, 268714, 4538209, 88188280, 1940666635, 47744244286, 1299383450941, 38777402351476, 1259552677645903, 44247546748659130, 1671904534990870369, 67624237153933934704, 2915628368081840175379, 133499617770334938670198 (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+2} which contain 2 fixed adjacent edges (i.e. a fixed K_{1,2}). For n=2, the a(2)=4 solutions are the 4 subtrees of K_4 which contain 2 fixed adjacent edges (i.e. those 2 edges, 1 copy of K_{1,3}, and 2 copies of P_4). - 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} 3*(n-k+3)^(n-k-1)*C(n, k).

E.g.f.: exp(x)*(-LambertW(-x)/x)^3.

a(n) ~ 3*exp(3+exp(-1))*n^(n-1). - Vaclav Kotesovec, Jul 08 2013

MAPLE

a:= n-> add(3*(n-j+3)^(n-j-1)*binomial(n, j), j=0..n):

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

MATHEMATICA

Table[Sum[3(n-k+3)^(n-k-1) Binomial[n, k], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Dec 04 2011 *)

CoefficientList[Series[E^x*(-LambertW[-x]/x)^3, {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)^3)) \\ G. C. Greubel, Nov 16 2017

CROSSREFS

Cf. A089461, A089463 (triangle).

Column k=3 of A144303.

Sequence in context: A184942 A000779 A053144 * A111343 A302908 A187123

Adjacent sequences:  A089461 A089462 A089463 * A089465 A089466 A089467

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 05 2003

STATUS

approved

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Last modified June 23 05:11 EDT 2021. Contains 345395 sequences. (Running on oeis4.)