login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A023877 Expansion of Product_{k>=1} (1 - x^k)^(-k^8). 4
1, 1, 257, 6818, 105250, 2175491, 44988020, 796565173, 13803604854, 240522266760, 4044067171130, 65769795259820, 1051279656603367, 16517653032316394, 254354069377336990, 3847172021760617755, 57300325471166205776, 840900188345961238222, 12164188625099191500782 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1170 (first 301 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(5 * Pi * 2^(17/10) * n^(9/10) / (3^(21/10) * 11^(1/10)) + 315*Zeta(9)/(4*Pi^8)) / (2^(13/20) * sqrt(5) * 33^(1/20) * n^(11/20)), where Zeta(9) = A013667 = 1.0020083928260822144... . - Vaclav Kotesovec, Feb 27 2015

G.f.: exp( Sum_{n>=1} sigma_9(n)*x^n/n ). - Seiichi Manyama, Mar 05 2017

a(n) = (1/n)*Sum_{k=1..n} sigma_9(k)*a(n-k). - Seiichi Manyama, Mar 05 2017

MAPLE

with(numtheory):

a:= proc(n) option remember; `if`(n=0, 1,

      add(add(d*d^8, d=divisors(j)) *a(n-j), j=1..n)/n)

    end:

seq(a(n), n=0..20);  # Alois P. Heinz, Nov 02 2012

MATHEMATICA

max = 18; Series[ Product[1/(1 - x^k)^k^8, {k, 1, max}], {x, 0, max}] // CoefficientList[#, x] & (* Jean-François Alcover, Mar 05 2013 *)

PROG

(PARI) m=20; x='x+O('x^m); Vec(prod(k=1, m, 1/(1-x^k)^k^8)) \\ G. C. Greubel, Oct 31 2018

(MAGMA) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[1/(1-x^k)^k^8: k in [1..m]]) )); // G. C. Greubel, Oct 31 2018

CROSSREFS

Column k=8 of A144048.

Sequence in context: A294303 A036086 A000542 * A301552 A279641 A168116

Adjacent sequences:  A023874 A023875 A023876 * A023878 A023879 A023880

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

Definition corrected by Franklin T. Adams-Watters and R. J. Mathar, Dec 04 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 19:24 EDT 2019. Contains 328127 sequences. (Running on oeis4.)