OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1093
P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Quebec, 1992, Vol. 16, No. 1, 53-80.
P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1, pp. 53-80, 1992. (Annotated scanned copy)
MAPLE
with(combstruct):B:=x->add(3*count([S, {B = Set(S), S = Prod(B, B, B, Z)}, unlabeled], size=i)*x^i, i=1..50); seq(coeff(B(x)-B(x)^2/2+B(x^2)/2, x, n)/3, n=1..30); # with Algolib (Pab Ter)
# Alternative:
b:= proc(n) option remember; `if`(n<2, 3*n, (add(add(b(d)
*d, d=numtheory[divisors](j))*b(n-j), j=1..n-1))/(n-1))
end:
a:= n-> `if`(n=0, 1, b(n)-(add(b(k) *b(n-k), k=0..n)-
`if`(irem(n, 2)=0, b(n/2), 0))/2)/3:
seq(a(n), n=1..30); # Alois P. Heinz, Jun 03 2020
MATHEMATICA
b[n_] := b[n] = If[n < 2, 3 n, (Sum[Sum[b[d] d, {d, Divisors[j]}] b[n - j], {j, 1, n - 1}])/(n - 1)];
a[n_] := If[n == 0, 1, b[n] - (Sum[b[k] b[n - k], {k, 0, n}] - If[Mod[n, 2] == 0, b[n/2], 0])/2]/3;
Array[a, 30] (* Jean-François Alcover, Nov 01 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved
