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A055349
Triangle of labeled mobiles (circular rooted trees) with n nodes and k leaves.
11
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
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.
Sequence in context: A095834 A106828 A055302 * A161174 A345422 A291240
KEYWORD
nonn,tabl,eigen
AUTHOR
Christian G. Bower, May 15 2000
STATUS
approved