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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A289571 Coefficients in expansion of q * Product_{n>=1} (1 - q^n)^24/E_6^(3/2). 1
1, 732, 483336, 299831152, 179912034330, 105705360893664, 61212394149183536, 35074084087016521152, 19935701871161896669257, 11259521840932766778870360, 6326766973556024191050129528, 3540038281600931271753859693440 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..366

M. Eichler and D. Zagier, On the zeros of the Weierstrass P-function, Math. Ann. 258 (1981/82), 399-407.

FORMULA

Sum_{n>=1} a(n)/n^2 * exp(-2*Pi*n) = (Pi - log(5+2*sqrt(6)))/(72*sqrt(6)).

a(n) ~ c * exp(2*Pi*n) * sqrt(n), where c = sqrt(2)/(432*sqrt(Pi)) = 0.001846955001858484620092342870066582724425271440578401192897804766993... - Vaclav Kotesovec, Jul 09 2017, updated Mar 05 2018

EXAMPLE

G.f.: q + 732*q^2 + 483336*q^3 + 299831152*q^4 + 179912034330*q^5 + ...

MATHEMATICA

nmax = 20; CoefficientList[Series[Product[(1 - x^k)^24, {k, 1, nmax}] / (1 - 504*Sum[DivisorSigma[5, k]*x^k, {k, 1, nmax}])^(3/2), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 09 2017 *)

CROSSREFS

Cf. A000594, A289570 (1/E_6^(3/2)).

Sequence in context: A031705 A158396 A098263 * A098291 A255798 A044988

Adjacent sequences:  A289568 A289569 A289570 * A289572 A289573 A289574

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jul 08 2017

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 December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)