

A038053


Number of labeled planted trees with 2colored leaves.


3



0, 4, 12, 96, 1120, 17280, 330624, 7540736, 199544832, 6006988800, 202646118400, 7570772656128, 310240496517120, 13834761553313792, 666909048381112320, 34555424387503226880, 1915099718255940468736
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index entries for sequences related to rooted trees


FORMULA

A038049 shifted right and multiplied by n.
E.g.f. (for offset 0): (2+B(x))*(xB(x))/(1+B(x)) where B(x) = LambertW(x*exp(x)).  Vladeta Jovovic, Mar 08 2003
a(n) ~ sqrt(LambertW(exp(1))+1) * n^(n1) / (exp(n) * (LambertW(exp(1)))^(n1)).  Vaclav Kotesovec, Mar 29 2014


MATHEMATICA

CoefficientList[Series[(2+LambertW[x*E^x])*(xLambertW[x*E^x])/(1+ LambertW[x*E^x]), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Mar 29 2014 *)


PROG

(PARI) x='x+O('x^30); concat([0], Vec(serlaplace( (2+lambertw(x*exp(x))) *(xlambertw(x*exp(x)))/(1+lambertw(x*exp(x))) ))) \\ G. C. Greubel, Sep 09 2018


CROSSREFS

Sequence in context: A074930 A287596 A268363 * A217155 A120267 A012278
Adjacent sequences: A038050 A038051 A038052 * A038054 A038055 A038056


KEYWORD

nonn


AUTHOR

Christian G. Bower, Jan 04 1999


STATUS

approved



