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A279758 Expansion of Product_{k>=1} 1/(1 - x^(k*(5*k^2-5*k+2)/2)).

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%I A279758 #8 May 08 2017 00:26:27
%S A279758 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 A279758 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 A279758 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 A279758 Expansion of Product_{k>=1} 1/(1 - x^(k*(5*k^2-5*k+2)/2)).
%C A279758 Number of partitions of n into nonzero icosahedral numbers (A006564).
%H A279758 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 A279758 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 A279758 OEIS Wiki, <a href="https://oeis.org/wiki/Platonic_numbers">Platonic numbers</a>
%H A279758 <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F A279758 G.f.: Product_{k>=1} 1/(1 - x^(k*(5*k^2-5*k+2)/2)).
%e A279758 a(13) = 2 because we have [12, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
%t A279758 nmax=105; CoefficientList[Series[Product[1/(1 - x^(k (5 k^2 - 5 k + 2)/2)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y A279758 Cf. A003108, A006564, A068980, A279757, A279759.
%K A279758 nonn
%O A279758 0,13
%A A279758 _Ilya Gutkovskiy_, Dec 18 2016