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

%I A218024 #14 May 08 2019 16:47:47
%S A218024 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,
%T A218024 956,1420,2117,3157,4721,7064,10597,15909,23933,36038,54356,82059,
%U A218024 124056,187707,284351,431114,654288,993780,1510785,2298471,3499653,5332313,8130576
%N A218024 Shifts 7 places left under Euler transform with a(0)=0 and a(n)=1 for n<7.
%H A218024 Alois P. Heinz, <a href="/A218024/b218024.txt">Table of n, a(n) for n = 0..1000</a>
%H A218024 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A218024 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
%p A218024 with(numtheory):
%p A218024 b:= proc(n) option remember; `if`(n=0, 1,
%p A218024       (add(add(d*a(d), d=divisors(j))*b(n-j), j=1..n))/n)
%p A218024     end:
%p A218024 a:= n-> `if`(n<7, signum(n), b(n-7)):
%p A218024 seq(a(n), n=0..50);
%Y A218024 Column k=7 of A144018.
%Y A218024 Cf. A316079.
%K A218024 nonn,eigen
%O A218024 0,10
%A A218024 _Alois P. Heinz_, Oct 18 2012