A055352 Number of labeled mobiles (circular rooted trees) with n nodes and 5 leaves.

144, 11508, 545664, 20469456, 678857760, 21047130720, 629779328640, 18547337128320, 544474197146880, 16067754570067200, 479436489384652800, 14522782898521497600, 447847214484186316800, 14087092606079728435200

Offset

6,1

Links

Georg Fischer, Table of n, a(n) for n = 6..250

Index entries for sequences related to mobiles

Formula

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

a(n) = (n!/5!) * stirling1(n-1,n-5) = n!*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(15*n^3-75*n^2+110*n-48)/691200.

E.g.f.: x^6*(24+58*x+22*x^2+x^3)/(120*(1-x)^9). (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, 5}] & /@ CoefficientList[A[x], x]) * Range[0, m - 1]!, 6] (* Jean-François Alcover, Nov 01 2019 *)

Crossrefs

Column 5 of A055349.

Sequence in context: A181014 A035821 A231854 * A381904 A199406 A182913

Adjacent sequences: A055349 A055350 A055351 * A055353 A055354 A055355

Keyword

nonn

Author

Christian G. Bower, May 15 2000

Status

approved