A218026 Shifts 9 places left under Euler transform with a(0)=0 and a(n)=1 for n<9.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 57, 80, 109, 152, 211, 296, 415, 588, 832, 1185, 1689, 2413, 3449, 4940, 7073, 10141, 14544, 20880, 29991, 43131, 62064, 89417, 128925, 186090, 268808, 388677, 562381, 814393, 1180070, 1711131

Offset: 0

Author

Alois P. Heinz, Oct 18 2012

Keywords

• nonn
• eigen

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Transforms

Crossrefs

Column k=9 of A144018.

Cf. A316081.

Programs

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1,
      (add(add(d*a(d), d=divisors(j)) *b(n-j), j=1..n))/n)
    end:
a:= n-> `if`(n<9, signum(n), b(n-9)):
seq(a(n), n=0..60);

Formula

G.f.: x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 / Product_{n>=1} (1 - x^n)^a(n). - Ilya Gutkovskiy, May 08 2019