%I #8 May 08 2017 00:26:27

%S 1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,

%T 3,3,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,

%U 8,8,8,8,10,10,10,10,10,10,10,10,10,10,10,10,12,12,12,12,12,12,12,12,12,12,12,12,15,15,15,15,15,15,15,15,15,15

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

%C Number of partitions of n into nonzero icosahedral numbers (A006564).

%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

%H OEIS Wiki, <a href="https://oeis.org/wiki/Platonic_numbers">Platonic numbers</a>

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

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

%e a(13) = 2 because we have [12, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

%t nmax=105; CoefficientList[Series[Product[1/(1 - x^(k (5 k^2 - 5 k + 2)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A003108, A006564, A068980, A279757, A279759.

%K nonn

%O 0,13

%A _Ilya Gutkovskiy_, Dec 18 2016