A218025 Shifts 8 places left under Euler transform with a(0)=0 and a(n)=1 for n<8.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 43, 59, 85, 118, 170, 241, 349, 500, 728, 1051, 1534, 2226, 3252, 4735, 6929, 10117, 14829, 21715, 31893, 46828, 68920, 101442, 149589, 220650, 325939, 481659, 712605, 1054747, 1562670, 2316296, 3436200

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=8 of A144018.

Cf. A316080.

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<8, signum(n), b(n-8)):
seq(a(n), n=0..50);

Formula

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