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

%I

%S 0,1,1,1,1,2,3,5,8,14,23,40,69,121,212,378,672,1208,2177,3946,7173,

%T 13104,23995,44103,81261,150149,278054,516141,959952,1788950,3339656,

%U 6245177,11696510,21938857,41206395,77496891,145926374,275098857,519181163,980848600

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

%H Alois P. Heinz, <a href="/A218020/b218020.txt">Table of n, a(n) for n = 0..1000</a>

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

%F a(n) ~ c * d^n / n^(3/2), where d = 1.964293016979213611214370656... and c = 0.8776048696248050091050307... . - _Vaclav Kotesovec_, Jun 23 2014

%F G.f.: x + x^2 + x^3 / 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<3, signum(n), b(n-3)):

%p seq(a(n), n=0..40);

%t 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-Fran├žois Alcover_, Aug 01 2013, after _Alois P. Heinz_ *)

%Y Column k=3 of A144018.

%Y Cf. A316075.

%K nonn,eigen

%O 0,6

%A _Alois P. Heinz_, Oct 18 2012

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Last modified April 15 13:37 EDT 2021. Contains 342977 sequences. (Running on oeis4.)