A055354 Number of labeled mobiles (circular rooted trees) with n nodes and 7 leaves.

5760, 940896, 85049280, 5731545600, 324745027200, 16481262283200, 778208622871680, 35036455255401600, 1529404526377728000, 65498410076875776000, 2775672164602681344000, 117137057625636739891200

Offset

8,1

Links

Georg Fischer, Table of n, a(n) for n = 8..250

Index entries for sequences related to mobiles

Formula

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

a(n) = (n!/7!) * stirling1(n-1,n-7) = n!*(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*(n-7)*(63*n^5-630*n^4+2205*n^3-3374*n^2+2296*n-576)/14631321600.

E.g.f.: x^8*(720+3708*x+4400*x^2+1452*x^3+114*x^4+x^5)/(5040*(1-x)^13). (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, 7}] & /@ CoefficientList[A[x], x]) * Range[0, m - 1]!, 8] (* Jean-François Alcover, Nov 01 2019 *)

Crossrefs

Column 7 of A055349.

Sequence in context: A190466 A157988 A330343 * A053862 A235393 A246421

Adjacent sequences: A055351 A055352 A055353 * A055355 A055356 A055357

Keyword

nonn

Author

Christian G. Bower, May 15 2000

Status

approved