A218024 Shifts 7 places left under Euler transform with a(0)=0 and a(n)=1 for n<7.

0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 22, 31, 45, 64, 94, 136, 200, 294, 435, 643, 956, 1420, 2117, 3157, 4721, 7064, 10597, 15909, 23933, 36038, 54356, 82059, 124056, 187707, 284351, 431114, 654288, 993780, 1510785, 2298471, 3499653, 5332313, 8130576

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=7 of A144018.

Cf. A316079.

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<7, signum(n), b(n-7)):
seq(a(n), n=0..50);

Formula

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