OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A027848(k)*a(n-k) for n > 0.
a(n) ~ exp((5*Pi)^(4/5) * Zeta(5)^(1/5) * n^(4/5) / (2^(8/5) * 3^(1/5)) - Zeta'(-3)/2) * Zeta(5)^(121/1200) / ((24*Pi)^(121/1200) * 5^(721/1200) * n^(721/1200)). - Vaclav Kotesovec, Mar 23 2018
G.f.: exp(Sum_{k>=1} sigma_4(k)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Oct 26 2018
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(
d*sigma[3](d), d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Jun 08 2017
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[1/(1-x^k)^DivisorSigma[3, k], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 23 2018 *)
PROG
(PARI) m=40; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-x^k)^sigma(k, 3))) \\ G. C. Greubel, Oct 30 2018
(Magma) m:=40; R<q>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-q^k)^DivisorSigma(3, k): k in [1..m]]) )); // G. C. Greubel, Oct 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 08 2017
STATUS
approved