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

%I A218025 #14 May 08 2019 16:47:07
%S A218025 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 A218025 728,1051,1534,2226,3252,4735,6929,10117,14829,21715,31893,46828,
%U A218025 68920,101442,149589,220650,325939,481659,712605,1054747,1562670,2316296,3436200
%N A218025 Shifts 8 places left under Euler transform with a(0)=0 and a(n)=1 for n<8.
%H A218025 Alois P. Heinz, <a href="/A218025/b218025.txt">Table of n, a(n) for n = 0..1000</a>
%H A218025 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A218025 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 A218025 with(numtheory):
%p A218025 b:= proc(n) option remember; `if`(n=0, 1,
%p A218025       (add(add(d*a(d), d=divisors(j))*b(n-j), j=1..n))/n)
%p A218025     end:
%p A218025 a:= n-> `if`(n<8, signum(n), b(n-8)):
%p A218025 seq(a(n), n=0..50);
%Y A218025 Column k=8 of A144018.
%Y A218025 Cf. A316080.
%K A218025 nonn,eigen
%O A218025 0,11
%A A218025 _Alois P. Heinz_, Oct 18 2012