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A218020 Shifts 3 places left under Euler transform with a(0)=0 and a(n)=1 for n < 3.

%I A218020 #20 May 08 2019 14:33:45
%S A218020 0,1,1,1,1,2,3,5,8,14,23,40,69,121,212,378,672,1208,2177,3946,7173,
%T A218020 13104,23995,44103,81261,150149,278054,516141,959952,1788950,3339656,
%U A218020 6245177,11696510,21938857,41206395,77496891,145926374,275098857,519181163,980848600
%N A218020 Shifts 3 places left under Euler transform with a(0)=0 and a(n)=1 for n < 3.
%H A218020 Alois P. Heinz, <a href="/A218020/b218020.txt">Table of n, a(n) for n = 0..1000</a>
%H A218020 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A218020 a(n) ~ c * d^n / n^(3/2), where d = 1.964293016979213611214370656... and c = 0.8776048696248050091050307... . - _Vaclav Kotesovec_, Jun 23 2014
%F A218020 G.f.: x + x^2 + x^3 / Product_{n>=1} (1 - x^n)^a(n). - _Ilya Gutkovskiy_, May 08 2019
%p A218020 with(numtheory):
%p A218020 b:= proc(n) option remember; `if`(n=0, 1,
%p A218020       (add(add(d*a(d), d=divisors(j)) *b(n-j), j=1..n))/n)
%p A218020     end:
%p A218020 a:= n-> `if`(n<3, signum(n), b(n-3)):
%p A218020 seq(a(n), n=0..40);
%t A218020 b[n_] := b[n] = If[n == 0, 1, (Sum[Sum[d*a[d], {d, Divisors[j]}]*b[n - j], {j, 1, n }])/n]; a[0] = 0; a[1] = a[2] = 1; a[n_] := b[n - 3]; Table[a[n], {n, 0, 39}] (* _Jean-François Alcover_, Aug 01 2013, after _Alois P. Heinz_ *)
%Y A218020 Column k=3 of A144018.
%Y A218020 Cf. A316075.
%K A218020 nonn,eigen
%O A218020 0,6
%A A218020 _Alois P. Heinz_, Oct 18 2012