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A218022 Shifts 5 places left under Euler transform with a(0)=0 and a(n)=1 for n<5.

%I A218022 #12 May 08 2019 16:28:48
%S A218022 0,1,1,1,1,1,1,2,3,5,7,11,16,25,38,59,91,143,223,352,555,881,1399,
%T A218022 2234,3569,5726,9197,14816,23901,38650,62583,101535,164948,268398,
%U A218022 437268,713379,1165156,1905348,3119012,5111199,8383837,13765016,22619804,37202634
%N A218022 Shifts 5 places left under Euler transform with a(0)=0 and a(n)=1 for n<5.
%H A218022 Alois P. Heinz, <a href="/A218022/b218022.txt">Table of n, a(n) for n = 0..1000</a>
%H A218022 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A218022 G.f.: x + x^2 + x^3 + x^4 + x^5 / Product_{n>=1} (1 - x^n)^a(n). - _Ilya Gutkovskiy_, May 08 2019
%p A218022 with(numtheory):
%p A218022 b:= proc(n) option remember; `if`(n=0, 1,
%p A218022       (add(add(d*a(d), d= divisors(j)) *b(n-j), j=1..n))/n)
%p A218022     end:
%p A218022 a:= n-> `if`(n<5, signum(n), b(n-5)):
%p A218022 seq(a(n), n=0..45);
%Y A218022 Column k=5 of A144018.
%Y A218022 Cf. A316077.
%K A218022 nonn,eigen
%O A218022 0,8
%A A218022 _Alois P. Heinz_, Oct 18 2012