A055355 Number of labeled mobiles (circular rooted trees) with n nodes and 8 leaves.

45360, 9862560, 1160973000, 99904860000, 7103580541200, 445556635524000, 25652184715357200, 1391455702596960000, 72404516222438400000, 3661224054771419136000, 181631020686490222848000

Offset

9,1

Links

Georg Fischer, Table of n, a(n) for n = 9..250

Index entries for sequences related to mobiles

Formula

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

a(n) = (n!/8!) * stirling1(n-1,n-8) = n!*(n-1)^2*(n-2)^2*(n-3)*(n-4)*(n-5)*(n-6)*(n-7)*(n-8)*(9*n^4-90*n^3+267*n^2-242*n+72)/234101145600.

E.g.f.: x^9*(5040+33984*x+58140*x^2+32120*x^3+5610*x^4+240*x^5+x^6)/(40320*(1-x)^15). (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, 8}] & /@ CoefficientList[A[x], x]) * Range[0, m - 1]!, 9] (* Jean-François Alcover, Nov 01 2019 *)

Crossrefs

Column 8 of A055349.

Sequence in context: A185927 A287378 A163816 * A210618 A269936 A269900

Adjacent sequences: A055352 A055353 A055354 * A055356 A055357 A055358

Keyword

nonn

Author

Christian G. Bower, May 15 2000

Status

approved