A279279 - OEIS

%I #5 Dec 10 2016 08:58:14

%S 1,1,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,1,1,0,0,0,0,0,1,1,0,0,0,0,

%T 1,1,0,0,0,0,0,0,0,1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0,0,2,2,

%U 0,0,0,0,1,2,1,0,0,0,0,1,1,1,1,0,0,0,0,1,2,1,0,1,1,0,2,2,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,1,2,1,0,1,1,1,1,1,2

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

%C Number of partitions of n into distinct hexagonal numbers (A000384).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal 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*(2*k-1))).

%e a(67) = 2 because we have [66, 1] and [45, 15, 6, 1].

%t nmax = 120; CoefficientList[Series[Product[1 + x^(k (2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000384, A024940, A033461, A218380, A278949, A279280, A279281.

%K nonn

%O 0,67

%A _Ilya Gutkovskiy_, Dec 09 2016