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Shifts 8 places left under Euler transform with a(0)=0 and a(n)=1 for n<8.
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%I #14 May 08 2019 16:47:07

%S 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,

%T 728,1051,1534,2226,3252,4735,6929,10117,14829,21715,31893,46828,

%U 68920,101442,149589,220650,325939,481659,712605,1054747,1562670,2316296,3436200

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

%H Alois P. Heinz, <a href="/A218025/b218025.txt">Table of n, a(n) for n = 0..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F 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

%p with(numtheory):

%p b:= proc(n) option remember; `if`(n=0, 1,

%p (add(add(d*a(d), d=divisors(j))*b(n-j), j=1..n))/n)

%p end:

%p a:= n-> `if`(n<8, signum(n), b(n-8)):

%p seq(a(n), n=0..50);

%Y Column k=8 of A144018.

%Y Cf. A316080.

%K nonn,eigen

%O 0,11

%A _Alois P. Heinz_, Oct 18 2012