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!)
A263147 Expansion of Product_{k>=1} (1+x^(5*k-3))^k. 6
1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 3, 0, 4, 0, 1, 4, 0, 10, 0, 6, 5, 0, 16, 0, 14, 6, 3, 28, 0, 32, 7, 10, 40, 0, 63, 8, 33, 60, 3, 112, 9, 74, 80, 14, 187, 10, 161, 110, 46, 300, 12, 308, 140, 120, 455, 24, 568, 182, 283, 672, 54, 968, 224, 594, 963, 146 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
LINKS
FORMULA
G.f.: exp(Sum_{j>=1} (-1)^(j+1)/j*x^(2*j)/(1 - x^(5*j))^2).
a(n) ~ 2^(43/100) * 3^(2/3) * 5^(2/3) * Zeta(3)^(1/6) * exp(-Pi^4/(3600*Zeta(3)) + Pi^2 * 3^(2/3) * 2^(1/3) * 5^(2/3) * n^(1/3) / (300*Zeta(3)^(1/3)) + Zeta(3)^(1/3) * 3^(4/3) * 2^(2/3) * 5^(1/3) * n^(2/3) / 20) / (30 * sqrt(Pi) * n^(2/3)).
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[(1+x^(5k-3))^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 100; CoefficientList[Series[E^Sum[(-1)^(j+1)/j*x^(2*j)/(1 - x^(5*j))^2, {j, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A128765 A193511 A254218 * A298100 A303636 A073274
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 10 2015
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 March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)