A218023 Shifts 6 places left under Euler transform with a(0)=0 and a(n)=1 for n<6.

0, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 23, 33, 50, 73, 112, 166, 254, 383, 587, 891, 1371, 2095, 3232, 4970, 7689, 11878, 18435, 28589, 44486, 69225, 107985, 168510, 263473, 412172, 645798, 1012516, 1589480, 2496956, 3926743, 6179504, 9733649, 15342313

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=6 of A144018.

Cf. A316078.

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<6, signum(n), b(n-6)):
seq(a(n), n=0..50);

Formula

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