a(0) = 1: {{}}.
a(1) = 1: {{a}}.
a(2) = 2: {{a,aa}, {a,ab}}.
a(3) = 1: {{a,aa,ab}}.
a(4) = 4: {{a,aa,ab,aaa}, {a,aa,ab,aab}, {a,aa,ab,aba}, {a,aa,ab,abc}}.
a(5) = 6: {{a,aa,ab,aaa,aab}, {a,aa,ab,aaa,aba}, {a,aa,ab,aaa,abc}, {a,aa,aab,aba}, {a,aa,ab,aab,ab,abc}, {a,aa,ab,aba,abc}}.
a(6) = 4: {{a,aa,ab,aaa,aab,aba}, {a,aa,ab,aaa,aab,abc}, {a,aa,ab,aaa,aba,abc}, {a,aa,ab,aab,aba,abc}}.
a(7) = 1: {{a,aa,ab,aaa,aab,aba,abc}}.
Breaking the sequence into lines after each 1 gives an irregular triangle whose j-th row equals the
A000085(j)-th row of
A007318 without its leftmost term. The leftmost column of this triangle is
A000085:
1;
1;
2, 1;
4, 6, 4, 1;
10, 45, 120, 210, 252, 210, 120, 45, 10, 1;
26, 325, 2600, 14950, 65780, 230230, 657800, 1562275, 3124550, ...
...
