OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Bernhard Heim, Markus Neuhauser, and Robert Troeger, Zeros Transfer For Recursively defined Polynomials, arXiv:2304.02694 [math.NT], 2023. See Table 5 p. 14.
FORMULA
a(n) = -Sum_{k=0..n-1} sigma(n-k)*a(k) for n>0 with a(0) = 1.
G.f.: 1/(1 + Sum_{k>=1} k*x^k/(1 - x^k)). - Ilya Gutkovskiy, Oct 18 2018
a(n) = Sum_{k=0..n} (-1)^k * A319083(n,k). - Alois P. Heinz, Feb 07 2025
EXAMPLE
G.f.: A(x) = 1 - x - 2*x^2 + x^3 + 2*x^4 + 4*x^5 - 6*x^6 - 5*x^7 + ...
1/A(x) = 1 - x*d/dx log(eta(x)) = 1 + x + 3*x^2 + 4*x^3 + 7*x^4 + ... + sigma(n)*x^n + ...
eta(x)^3/A(x) = 1 - 2*x + 7*x^6 - 21*x^10 + 44*x^15 - 78*x^21 + ... + A184366(n)*x^n + ...
PROG
(PARI) lista(nn) = {va = vector(nn); va[1] = 1; for (n=1, nn-1, va[n+1] = -sum(k=0, n-1, sigma(n-k)*va[k+1]); ); va; } \\ Michel Marcus, Mar 05 2017
CROSSREFS
KEYWORD
sign,changed
AUTHOR
Seiichi Manyama, Mar 05 2017
STATUS
approved