A279762 Expansion of Product_{k>=1} 1/(1 - x^k)^(k*(5*k^2-5*k+2)/2).

1, 1, 13, 61, 263, 1094, 4578, 18076, 69815, 262242, 965342, 3480006, 12322360, 42896002, 147062818, 497000146, 1657470977, 5459160063, 17772284155, 57225458626, 182362100816, 575463112191, 1799106136923, 5575063264825, 17130798464652, 52216240087807, 157937816918539, 474197830869573, 1413695306175884, 4185962563381518

Offset

0,3

Comments

Euler transform of the icosahedral numbers (A006564).

Links

Table of n, a(n) for n=0..29.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

N. J. A. Sloane, Transforms

OEIS Wiki, Platonic numbers

Formula

G.f.: Product_{k>=1} 1/(1 - x^k)^(k*(5*k^2-5*k+2)/2).

a(n) ~ exp(Zeta'(-1) + 5*Zeta(3) / (8*Pi^2) - Pi^16 / (16796160000*Zeta(5)^3) + Pi^8 * Zeta(3) / (648000*Zeta(5)^2) - Zeta(3)^2 / (150*Zeta(5)) + 5*Zeta'(-3)/2 + (-Pi^12/(19440000 * 2^(2/5) * 15^(1/5) * Zeta(5)^(11/5)) + Pi^4 * Zeta(3) / (900 * 2^(2/5) * 15^(1/5) * Zeta(5)^(6/5))) * n^(1/5) + (-Pi^8 / (21600 * 2^(4/5) * 15^(2/5) * Zeta(5)^(7/5)) + Zeta(3) / (2^(4/5) * (15*Zeta(5))^(2/5))) * n^(2/5) + (-Pi^4 / (36 * 2^(1/5) * (15*Zeta(5))^(3/5))) * n^(3/5) + ((5*(15*Zeta(5))^(1/5)) / 2^(8/5)) * n^(4/5)) * (3*Zeta(5))^(9/80) / (2^(11/40) * 5^(31/80) * sqrt(Pi) * n^(49/80)). - Vaclav Kotesovec, Nov 09 2017

Mathematica

nmax=29; CoefficientList[Series[Product[1/(1 - x^k)^(k (5 k^2 - 5 k + 2)/2), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000335, A006564, A023872.

Sequence in context: A047673 A231800 A141725 * A147185 A122885 A257216

Adjacent sequences: A279759 A279760 A279761 * A279763 A279764 A279765

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 18 2016

Status

approved