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%I #9 Apr 21 2017 04:39:03
%S 1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,
%T 0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,1,0,
%U 0,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,1,2,1,0,0,0,0,0,0,1,1,0,0,1,1
%N Expansion of Product_{k>=1} (1 + x^(k*(3*k-2))).
%C Number of partitions of n into distinct octagonal numbers (A000567).
%H G. C. Greubel, <a href="/A279281/b279281.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} (1 + x^(k*(3*k-2))).
%e a(105) = 2 because we have [96, 8, 1] and [65, 40].
%t nmax = 120; CoefficientList[Series[Product[1 + x^(k (3 k - 2)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000567, A024940, A033461, A218380, A279041, A279279, A279280.
%K nonn
%O 0,106
%A _Ilya Gutkovskiy_, Dec 09 2016
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