OFFSET
0,3
COMMENTS
One of the components may be empty (the null graph): a(n) = A000055(n) + A274937(n). - R. J. Mathar, Aug 15 2017
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: [A(x)^2 + A(x^2)]/2 where A(x) is the o.g.f. for A000055.
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n<2, n, (add(add(d*
b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))
end:
g:= proc(n) option remember; `if`(n=0, 1, b(n)-add(b(j)*
b(n-j), j=0..n/2)+`if`(n::odd, 0, (t->t*(t+1)/2)(b(n/2))))
end:
a:= proc(n) option remember; add(g(j)*g(n-j), j=0..n/2)-
`if`(n::odd, 0, (t-> t*(t-1)/2)(g(n/2)))
end:
seq(a(n), n=0..40); # Alois P. Heinz, Jul 20 2016
MATHEMATICA
b[n_] := b[n] = If[n<2, n, Sum[DivisorSum[j, #*b[#]&]*b[n-j], {j, 1, n-1}]/ (n-1)];
g[n_] := g[n] = If[n==0, 1, b[n]-Sum[b[j]*b[n-j], {j, 0, n/2}]+If[OddQ[n], 0, Function[t, t*(t+1)/2][b[n/2]]]];
a[n_] := a[n] = Sum[g[j]*g[n-j], {j, 0, n/2}]-If[OddQ[n], 0, Function[t, t*(t-1)/2][g[n/2]]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 15 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 19 2016
STATUS
approved