OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..5402
FORMULA
a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A288420(k)*a(n-k) for n > 0.
a(n) ~ exp(5*Pi^(4/5) * Zeta(5)^(1/5) * n^(4/5) / 2^(12/5)) * Zeta(5)^(1/10) / (2^(169/240) * sqrt(5) * Pi^(1/10) * n^(3/5)). - Vaclav Kotesovec, Mar 23 2018
G.f.: Product_{i>=1, j>=1} (1 + x^(i*j))^(j^3). - Ilya Gutkovskiy, Aug 26 2018
MAPLE
with(numtheory): seq(coeff(series(mul((1+x^k)^(sigma[3](k)), k=1..n), x, n+1), x, n), n = 0 .. 30); # Muniru A Asiru, Oct 31 2018
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[(1+x^k)^DivisorSigma[3, k], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 09 2017 *)
PROG
(PARI) m=40; x='x+O('x^m); Vec(prod(k=1, m, (1+x^k)^sigma(k, 3))) \\ G. C. Greubel, Oct 30 2018
(Magma) m:=40; R<q>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[(1+q^k)^DivisorSigma(3, k): k in [1..m]]) )); // G. C. Greubel, Oct 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 09 2017
STATUS
approved