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
Examples
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;
...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)
- Index entries for sequences related to mobiles
Crossrefs
Programs
-
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 *) -
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
Formula
E.g.f. satisfies A(x, y) = x*y - x*log(1-A(x, y)). [Corrected by Sean A. Irvine, Mar 19 2022]