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

0, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 16, 25, 38, 59, 91, 143, 223, 352, 555, 881, 1399, 2234, 3569, 5726, 9197, 14816, 23901, 38650, 62583, 101535, 164948, 268398, 437268, 713379, 1165156, 1905348, 3119012, 5111199, 8383837, 13765016, 22619804, 37202634

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Formula

G.f.: x + x^2 + x^3 + x^4 + x^5 / Product_{n>=1} (1 - x^n)^a(n). - Ilya Gutkovskiy, May 08 2019

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<5, signum(n), b(n-5)):
seq(a(n), n=0..45);

Crossrefs

Column k=5 of A144018.

Cf. A316077.

Sequence in context: A018057 A355907 A130137 * A374151 A091980 A274113

Adjacent sequences: A218019 A218020 A218021 * A218023 A218024 A218025

Keyword

nonn,eigen

Author

Alois P. Heinz, Oct 18 2012

Status

approved