[go: up one dir, main page]
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A292547 Number of partitions of n into distinct odd cubes. 4
1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0
COMMENTS
In general, if m > 0 and g.f. = Product_{k>=1} (1 + x^((2*k-1)^m)), then a(n) ~ exp((m+1) * ((2^(1/m)-1) * Gamma(1/m) * Zeta(1+1/m) / m^2)^(m/(m+1)) * n^(1/(m+1)) / 2) * ((2^(1/m)-1) * Gamma(1/m) * Zeta(1+1/m))^(m/(2*(m+1))) / (2*sqrt(Pi*(m+1)) * m^((m-1)/(2*(m+1))) * n^((2*m+1)/(2*(m+1)))).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..100000
Vaclav Kotesovec, Graph - The asymptotic ratio
FORMULA
G.f.: Product_{k>=1} (1 + x^((2*k-1)^3)).
a(n) ~ exp(2 * 3^(-3/2) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/4) * n^(1/4)) * ((2^(1/3)-1) * Gamma(1/3) * Zeta(4/3))^(3/8) / (4*3^(1/4) * sqrt(Pi) * n^(7/8)).
MATHEMATICA
nmax = 200; CoefficientList[Series[Product[1 + x^((2*k-1)^3), {k, 1, Floor[nmax^(1/3)/2] + 1}], {x, 0, nmax}], x]
CROSSREFS
Cf. A000700 (m=1), A167700 (m=2).
Cf. A033461, A279329, A287091, A290276, A292740.
Sequence in context: A014071 A014038 A014067 * A014032 A014055 A256433
Adjacent sequences: A292544 A292545 A292546 * A292548 A292549 A292550
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 18 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 29 21:13 EDT 2024. Contains 375518 sequences. (Running on oeis4.)