A397737 Number of assembly trees for the wheel graph W_n.

3, 15, 78, 435, 2658, 18102, 138780, 1198971, 11600730, 124489794, 1466798916, 18807464910, 260499759828, 3874067519820, 61547871299640, 1040102328321675, 18626778871389450, 352351829564950410

Offset

3,1

Comments

For n >= 4, the wheel graph W_n has n vertices and is the join of a cycle C_{n-1} and a singleton.

The sequence is extended to a(3) using the formula.

Links

Table of n, a(n) for n=3..20.

Eric Weisstein's World of Mathematics, Assembly Number.

Eric Weisstein's World of Mathematics, Wheel Graph.

Formula

a(n) = binomial(2*n-4,n-2)*(1/2 + hypergeom([1,3,3-n],[5-2*n],1)).

With m = n - 1, a(n) = binomial(2*m-2,m-1)/2 + m*Sum_{b=2..m} b!*binomial(2*m-b,m-b)/(2*m-b).

Mathematica

Table[Binomial[2 n - 4, n - 2] (1/2 + HypergeometricPFQ[{1, 3, 3 - n}, {5 - 2 n}, 1]), {n, 3, 20}]

Crossrefs

Sequence in context: A125700 A227954 A104530 * A297952 A298771 A298576

Adjacent sequences: A397732 A397733 A397735 * A397738 A397741 A397743

Keyword

nonn,new

Author

Eric W. Weisstein, Jul 08 2026

Status

approved