A055349 Triangle of labeled mobiles (circular rooted trees) with n nodes and k leaves.

1, 2, 0, 6, 3, 0, 24, 36, 8, 0, 120, 360, 220, 30, 0, 720, 3600, 4200, 1500, 144, 0, 5040, 37800, 71400, 47250, 11508, 840, 0, 40320, 423360, 1176000, 1234800, 545664, 98784, 5760, 0, 362880, 5080320, 19474560, 29635200, 20469456, 6618528, 940896, 45360, 0

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Index entries for sequences related to mobiles

Formula

E.g.f. satisfies A(x, y) = x*y - x*log(1-A(x, y)). [Corrected by Sean A. Irvine, Mar 19 2022]

Example

Triangle begins:
     1;
     2,     0;
     6,     3,     0;
    24,    36,     8,     0;
   120,   360,   220,    30,     0;
   720,  3600,  4200,  1500,   144,   0;
  5040, 37800, 71400, 47250, 11508, 840, 0;
  ...

Mathematica

T[rows_] := {{1}}~Join~((cc = CoefficientList[#, y]; Append[Rest[cc], 0] * Length[cc]!)& /@ (CoefficientList[InverseSeries[x/(y-Log[1-x + O[x]^rows] ), x], x][[3;; ]]));
T[9] // Flatten (* Jean-François Alcover, Oct 31 2019 *)

Prog

(PARI)
A(n)={my(v=Vec(serlaplace(serreverse(x/(y - log(1-x + O(x^n))))))); vector(#v, i, Vecrev(v[i]/y, i))}
{ my(T=A(10)); for(i=1, #T, print(T[i])) } \\ Andrew Howroyd, Sep 23 2018

Crossrefs

Row sums give A038037.

Columns 1..8 are A000142, A055303, A055350, A055351, A055352, A055353, A055354, A055355.

Cf. A055340, A055356, A055363.

Sequence in context: A095834 A106828 A055302 * A161174 A345422 A291240

Adjacent sequences: A055346 A055347 A055348 * A055350 A055351 A055352

Keyword

nonn,tabl,eigen

Author

Christian G. Bower, May 15 2000

Status

approved