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%I #8 May 08 2017 00:26:50
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T 2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,
%U 4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9
%N Expansion of Product_{k>=1} 1/(1 - x^(k*(3*k-1)*(3*k-2)/2)).
%C Number of partitions of n into nonzero dodecahedral numbers (A006566).
%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*(3*k-1)*(3*k-2)/2)).
%e a(21) = 2 because we have [20, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
%t nmax=120; CoefficientList[Series[Product[1/(1 - x^(k (3 k - 1) (3 k - 2)/2)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A003108, A006566, A068980, A279757, A279758.
%K nonn
%O 0,21
%A _Ilya Gutkovskiy_, Dec 18 2016