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Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)*(k+2)*(k+3)/24)).
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%I #30 Aug 15 2017 20:36:54

%S 1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,5,5,5,5,5,7,7,7,7,7,9,9,9,9,9,12,12,12,

%T 12,12,16,16,16,16,16,20,20,20,20,20,25,25,25,25,25,31,31,31,31,31,37,

%U 37,37,37,37,44,44,44,44,44,52,52,52,52,52,62,62,62,62,62,73,73,73,73,73,85,85,85,85,85,99

%N Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)*(k+2)*(k+3)/24)).

%C Number of partitions of n into nonzero 4-dimensional pyramidal numbers (A000332).

%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=1} 1/(1 - x^(k*(k+1)*(k+2)*(k+3)/24)).

%e a(10) = 3 because we have [5, 5], [5, 1, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].

%t nmax = 85; CoefficientList[Series[Product[1/(1 - x^(k (k + 1) (k + 2) (k + 3)/24)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000292, A000332, A007294, A068980, A290792.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Aug 15 2017