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 A298935 Number of partitions of n^3 into distinct squares. 4

%I

%S 1,1,0,0,1,5,8,40,96,297,1269,3456,12839,46691,153111,577167,2054576,

%T 7602937,29000337,110645967,418889453,1580667760,6058528796,

%U 23121913246,89793473393,350029321425,1359919742613,5340642744919,20948242218543,82505892314268

%N Number of partitions of n^3 into distinct squares.

%H Alois P. Heinz, <a href="/A298935/b298935.txt">Table of n, a(n) for n = 0..80</a>

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

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

%F a(n) = [x^(n^3)] Product_{k>=1} (1 + x^(k^2)).

%F a(n) = A033461(A000578(n)).

%e a(5) = 5 because we have [121, 4], [100, 25], [100, 16, 9], [64, 36, 25] and [64, 36, 16, 9].

%t Table[SeriesCoefficient[Product[1 + x^k^2, {k, 1, Floor[n^(3/2) + 1]}], {x, 0, n^3}], {n, 0, 29}]

%Y Cf. A000290, A000578, A030272, A030273, A033461, A037444, A218494, A298330, A298642, A298934.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Jan 29 2018

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Last modified April 3 20:29 EDT 2020. Contains 333199 sequences. (Running on oeis4.)