A218027 Shifts 10 places left under Euler transform with a(0)=0 and a(n)=1 for n<10.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 78, 104, 143, 193, 266, 362, 503, 693, 969, 1349, 1896, 2656, 3746, 5267, 7436, 10476, 14798, 20869, 29491, 41635, 58878, 83234, 117841, 166851, 236568, 335526, 476451, 676868, 962566

Offset: 0

Author

Alois P. Heinz, Oct 18 2012

Keywords

• nonn
• eigen

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Transforms

Crossrefs

Column k=10 of A144018.

Cf. A316082.

Programs

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<10, signum(n), b(n-10)):
seq(a(n), n=0..60);

Formula

G.f.: x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 / Product_{n>=1} (1 - x^n)^a(n). - Ilya Gutkovskiy, May 08 2019