OFFSET
1,3
COMMENTS
Eigensequence of triangle A126988. (i.e. the sequence shifts upon multiplication from the left by triangle A126988). - Gary W. Adamson, Apr 27 2009
Number of planted achiral trees with a distinguished leaf. - Gus Wiseman, Jul 31 2018
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
FORMULA
a(1) = 1; a(n > 1) = Sum_{d|(n-1)} d * a((n-1)/d). - Gus Wiseman, Jul 31 2018
G.f. A(x) satisfies: A(x) = x * (1 + Sum_{j>=1} j*A(x^j)). - Ilya Gutkovskiy, May 09 2019
EXAMPLE
From Gus Wiseman, Jul 31 2018: (Start)
The a(5) = 12 planted achiral trees with a distinguished leaf:
(Oooo), (oOoo), (ooOo), (oooO),
((O)(o)), ((o)(O)),
((Ooo)), ((oOo)), ((ooO)),
(((Oo))), (((oO))),
((((O)))).
(End)
MAPLE
a:= proc(n) option remember; `if`(n<2, n, (m-> m*
add(a(d)/d, d=numtheory[divisors](m)))(n-1))
end:
seq(a(n), n=1..50); # Alois P. Heinz, May 09 2019
MATHEMATICA
a[n_]:=If[n==1, 1, Sum[d*a[(n-1)/d], {d, Divisors[n-1]}]];
Array[a, 30] (* Gus Wiseman, Jul 31 2018 *)
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
STATUS
approved