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%I #8 May 08 2017 00:22:49
%S 1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,5,5,5,5,5,5,7,7,7,7,7,7,9,9,9,9,
%T 9,9,12,12,12,12,13,13,16,16,16,16,17,17,20,20,20,20,21,21,25,25,25,
%U 25,27,27,31,31,31,31,33,33,37,37,37,37,39,39,44,44,44,45,48,48,53,53,54,55,58,58,63,63,64,65,68,68,74
%N Expansion of Product_{k>=1} 1/(1 - x^(k^2*(k+1)/2)).
%C Number of partitions of n into nonzero pentagonal pyramidal numbers (A002411).
%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/PentagonalPyramidalNumber.html">Pentagonal 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^2*(k+1)/2)).
%e a(7) = 2 because we have [6, 1] and [1, 1, 1, 1, 1, 1, 1].
%t nmax=90; CoefficientList[Series[Product[1/(1 - x^(k^2 (k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A002411, A068980, A279220, A279222, A279223, A279224.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Dec 08 2016
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