A055350 Number of labeled mobiles (circular rooted trees) with n nodes and 3 leaves.

8, 220, 4200, 71400, 1176000, 19474560, 330220800, 5787936000, 105380352000, 1997835840000, 39477236198400, 813155511168000, 17453093898240000, 390070546145280000, 9070029416448000000, 219204470936715264000

Offset

4,1

Links

Georg Fischer, Table of n, a(n) for n = 4..250

Index entries for sequences related to mobiles

Formula

From Natalia L. Skirrow, Nov 30 2025: (Start)

a(n) = (n!/3!) * stirling1(n-1,n-3) = n!*(n-1)*(n-2)*(n-3)*(3*n-4)/144.

E.g.f.: x^4*(2+x)/(6*(1-x)^5). (End)

Mathematica

m = 20;
L[x_] = Log[1-x] + O[x]^m // Normal;
A[_] = 0;
Do[A[x_] = x y - x L[A[x]] + O[x]^k // Normal // Expand, {k, m}];
Drop[(SeriesCoefficient[#, {y, 0, 3}]& /@ CoefficientList[A[x], x]) * Range[0, m-1]!, 4] (* Jean-François Alcover, Nov 01 2019 *)

Crossrefs

Column 3 of A055349.

Sequence in context: A305517 A298964 A298455 * A183261 A316954 A299734

Adjacent sequences: A055347 A055348 A055349 * A055351 A055352 A055353

Keyword

nonn

Author

Christian G. Bower, May 15 2000

Status

approved