OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..3339 (first 801 terms from Alois P. Heinz)
G. Almkvist, Asymptotic formulas and generalized Dedekind sums, Exper. Math., 7 (No. 4, 1998), pp. 343-359.
Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 21.
FORMULA
a(n) ~ exp(Pi * 2^(3/2) * 3^(2/3) * n^(5/6) / (5 * 7^(1/6)) + 3*Zeta(5) / (4*Pi^4)) / (2^(3/4) * 3^(2/3) * 7^(1/12) * n^(7/12)), where Zeta(5) = A013663 = 1.036927755143369926... . - Vaclav Kotesovec, Feb 27 2015
G.f.: exp( Sum_{n>=1} sigma_5(n)*x^n/n ). - Seiichi Manyama, Mar 04 2017
a(n) = (1/n)*Sum_{k=1..n} sigma_5(k)*a(n-k). - Seiichi Manyama, Mar 04 2017
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1,
add(add(d*d^4, d=divisors(j)) *a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..25); # Alois P. Heinz, Nov 02 2012
MATHEMATICA
max = 27; Series[ Product[1/(1 - x^k)^k^4, {k, 1, max}], {x, 0, max}] // CoefficientList[#, x] & (* Jean-François Alcover, Mar 05 2013 *)
PROG
(PARI) m=30; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-x^k)^k^4)) \\ G. C. Greubel, Oct 30 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^k^4: k in [1..m]]) )); // G. C. Greubel, Oct 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition corrected by Franklin T. Adams-Watters and R. J. Mathar, Dec 04 2006
STATUS
approved