The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A304873 G.f.: Sum_{k>=0} p(k)^4 * x^k / Sum_{k>=0} p(k)*x^k, where p(n) is the partition function A000041(n). 6
 1, 0, 14, 64, 528, 1696, 11616, 33600, 169072, 525760, 2069922, 5928066, 22259874, 59321760, 193797792, 526647420, 1566376990, 4012181104, 11456306798, 28263784110, 75995086336, 184440427360, 468750673616, 1104027571108, 2730165482640, 6239956155696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS In general, if m > 1 and g.f. = Sum_{k>=0} p(k)^m * x^k / Sum_{k>=0} p(k)*x^k, then a(n, m) ~ exp(Pi*sqrt(2*(m^2 - 1)*n/3)) * ((m^2 - 1)^(m - 3/4) / (2^(2*m - 3/4) * 3^(m/2 - 1/4) * m^(2*m - 1) * n^(m - 1/4))). LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA a(n) ~ 2^(3/4) * 3^(3/2) * 5^(13/4) * exp(Pi*sqrt(10*n)) / (2^22 * n^(15/4)). MATHEMATICA nmax = 25; CoefficientList[Series[Sum[PartitionsP[k]^4*x^k, {k, 0, nmax}] / Sum[PartitionsP[k]*x^k, {k, 0, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A054440 (m=2), A260664 (m=3). Cf. A000041, A001255, A133042, A304877, A304878. Sequence in context: A124892 A126401 A275268 * A226754 A058092 A213757 Adjacent sequences: A304870 A304871 A304872 * A304874 A304875 A304876 KEYWORD nonn AUTHOR Vaclav Kotesovec, May 20 2018 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.

Last modified September 16 17:53 EDT 2024. Contains 375976 sequences. (Running on oeis4.)