%I
%S 1,15,105,455,1365,3003,5005,6435,6435,5005,3003,1365,470,315,1380,
%T 5461,15015,30030,45045,51480,45045,30030,15015,5460,1470,1575,8205,
%U 30030,75075,135135,180180,180180,135135,75075,30030,8190,1820,5565,30030,100100,225225,360360,420420,360360,225225,100100,30030,5460
%N Expansion of (Sum_{k>=0} x^(k*(5*k^25*k+2)/2))^15.
%C Number of ways to write n as an ordered sum of 15 icosahedral numbers (A006564).
%C Pollock conjectured that every number is the sum of at most 5 tetrahedral numbers and that every number is the sum of at most 7 octahedral numbers.
%C Conjecture: a(n) > 0 for all n >= 0.
%C Extended conjecture: every number is the sum of at most 15 icosahedral numbers.
%H Ilya Gutkovskiy, <a href="/A282350/a282350.pdf">Extended graphical example</a>
%F G.f.: (Sum_{k>=0} x^(k*(5*k^25*k+2)/2))^15.
%t nmax = 47; CoefficientList[Series[Sum[x^(k (5 k^2  5 k + 2)/2), {k, 0, nmax}]^15, {x, 0, nmax}], x]
%Y Cf. A006564, A282172, A282349.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Feb 12 2017
