A218020 Shifts 3 places left under Euler transform with a(0)=0 and a(n)=1 for n < 3.
0, 1, 1, 1, 1, 2, 3, 5, 8, 14, 23, 40, 69, 121, 212, 378, 672, 1208, 2177, 3946, 7173, 13104, 23995, 44103, 81261, 150149, 278054, 516141, 959952, 1788950, 3339656, 6245177, 11696510, 21938857, 41206395, 77496891, 145926374, 275098857, 519181163, 980848600
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- N. J. A. Sloane, Transforms
Programs
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Maple
with(numtheory): b:= proc(n) option remember; `if`(n=0, 1, (add(add(d*a(d), d=divisors(j)) *b(n-j), j=1..n))/n) end: a:= n-> `if`(n<3, signum(n), b(n-3)): seq(a(n), n=0..40); -
Mathematica
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 *)
Formula
a(n) ~ c * d^n / n^(3/2), where d = 1.964293016979213611214370656... and c = 0.8776048696248050091050307... . - Vaclav Kotesovec, Jun 23 2014
G.f.: x + x^2 + x^3 / Product_{n>=1} (1 - x^n)^a(n). - Ilya Gutkovskiy, May 08 2019