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%I #8 May 08 2017 00:23:05
%S 1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,5,5,5,5,5,5,6,7,7,7,7,7,
%T 7,8,9,9,9,9,9,9,10,11,12,12,12,12,12,13,15,16,16,16,16,16,17,19,20,
%U 20,20,20,20,21,23,24,25,25,25,25,26,28,30,31,31,31,31,32,34,36,37,37,37,37,38,40,42,43,44,44,44
%N Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)*(4*k-1)/6)).
%C Number of partitions of n into nonzero hexagonal pyramidal numbers (A002412).
%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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexagonalPyramidalNumber.html">Hexagonal Pyramidal Number</a>
%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal 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*(k+1)*(4*k-1)/6)).
%e a(8) = 2 because we have [7, 1] and [1, 1, 1, 1, 1, 1, 1, 1].
%t nmax=90; CoefficientList[Series[Product[1/(1 - x^(k (k + 1) (4 k - 1)/6)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A002412, A068980, A279220, A279221, A279223, A279224.
%K nonn
%O 0,8
%A _Ilya Gutkovskiy_, Dec 08 2016
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