OFFSET
1,5
REFERENCES
F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973, page 57.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
Charlie Liou and Anthony Mendes, Matrix Representations From Labeled Trees, J. Int. Seq. (2023) Vol. 26, No. 7, Article 23.7.6.
FORMULA
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n<=1, n,
(add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))
end:
a:= proc(n) option remember; (add(b(k)*b(n-1-k), k=0..n-1)-
`if`(irem(n, 2, 'r')=1, b(r), 0))/2
end:
seq(a(n), n=1..50); # Alois P. Heinz, May 16 2013
MATHEMATICA
Needs["Combinatorica`"]
nn=30; s[n_, k_]:=s[n, k]=a[n+1-k]+If[n<2k, 0, s[n-k, k]]; a[1]=1; a[n_]:=a[n]=Sum[a[i]s[n-1, i]i, {i, 1, n-1}]/(n-1); rt=Table[a[i], {i, 1, nn}]; Take[CoefficientList[CycleIndex[AlternatingGroup[2], s]-CycleIndex[SymmetricGroup[2], s]/.Table[s[j]->Table[Sum[rt[[i]]x^(i*k), {i, 1, nn}], {k, 1, nn}][[j]], {j, 1, nn}], x], nn] (* after code by Robert A. Russell in A000081 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 19 2012
STATUS
approved