OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..3213
EXAMPLE
a(0) = 1: {}.
a(1) = 1: {1}.
a(2) = 4: {01}, {10}, {11}, {1,1}.
a(3) = 8: {011}, {101}, {110}, {111}, {1,01}, {1,10}, {1,11}, {1,1,1}.
MAPLE
g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
g(d), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..35);
MATHEMATICA
g[n_] := 2^(n-1) + If[OddQ[n], 0, Binomial[n, n/2]/2];
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*
g[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Apr 30 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 18 2017
STATUS
approved