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A300974 a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^2))^n.

%I A300974 #10 Mar 23 2018 05:31:55
%S A300974 1,1,3,10,39,151,588,2304,9111,36307,145553,586246,2370264,9614242,
%T A300974 39105580,159444160,651468967,2666771488,10934393619,44899828056,
%U A300974 184616878289,760010818689,3132147583744,12921037206764,53351800567200,220478125956426,911839751015196,3773836780169050
%N A300974 a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^2))^n.
%C A300974 Number of partitions of n into squares of n kinds.
%H A300974 Vaclav Kotesovec, <a href="/A300974/b300974.txt">Table of n, a(n) for n = 0..500</a>
%H A300974 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A300974 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A300974 From _Vaclav Kotesovec_, Mar 23 2018: (Start)
%F A300974 a(n) ~ c * d^n / sqrt(n), where
%F A300974 d = 4.216358447600641565890184638418336163396695730036... and
%F A300974 c = 0.26442245016754864773722176155288663999776... (End)
%p A300974 a:= proc(m) option remember; local b; b:= proc(n, i)
%p A300974       option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A300974       binomial(m+j-1, j)*b(n-i^2*j, i-1), j=0..n/i^2)))
%p A300974       end: b(n, isqrt(n))
%p A300974     end:
%p A300974 seq(a(n), n=0..30);  # _Alois P. Heinz_, Mar 17 2018
%t A300974 Table[SeriesCoefficient[Product[1/(1 - x^k^2)^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]
%Y A300974 Cf. A000290, A001156, A008485, A023871, A240944, A279225, A285047, A300975, A301518.
%K A300974 nonn
%O A300974 0,3
%A A300974 _Ilya Gutkovskiy_, Mar 17 2018