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%I #15 Jan 16 2024 17:32:56
%S 1,1,2,2,4,2,10,2,17,14,33,2,167,2,186,491,785,2,5839,2,11123,53454,
%T 15229,2,1102924,53537,193382,16334183,12411062,2,382413555,2,
%U 993814248,9763321547,53394774,1778595972,402119882757,2,1111261718,9674133468473,16955983996383
%N Number of non-isomorphic set-systems of weight n in which all parts have the same size.
%C A set-system of weight n is a finite set of finite nonempty sets whose sizes sum to n.
%H Andrew Howroyd, <a href="/A306019/b306019.txt">Table of n, a(n) for n = 0..50</a>
%F a(p) = 2 for prime p. - _Andrew Howroyd_, Aug 29 2019
%F a(n) = Sum_{d|n} A331508(n/d, d) for n > 0. - _Andrew Howroyd_, Jan 16 2024
%e Non-isomorphic representatives of the a(6) = 10 set-systems:
%e {{1,2,3,4,5,6}}
%e {{1,2,3},{4,5,6}}
%e {{1,2,5},{3,4,5}}
%e {{1,3,4},{2,3,4}}
%e {{1,2},{1,3},{2,3}}
%e {{1,2},{3,4},{5,6}}
%e {{1,2},{3,5},{4,5}}
%e {{1,3},{2,4},{3,4}}
%e {{1,4},{2,4},{3,4}}
%e {{1},{2},{3},{4},{5},{6}}
%o (PARI) \\ See A331508 for T(n,k).
%o a(n) = {if(n==0, 1, sumdiv(n, d, if(d==1 || d==n, 1, T(n/d, d))))} \\ _Andrew Howroyd_, Jan 16 2024
%Y Cf. A000005, A001315, A007716, A038041, A049311, A283877, A298422, A306017, A306018, A306020, A306021.
%K nonn
%O 0,3
%A _Gus Wiseman_, Jun 17 2018
%E Terms a(12) and beyond from _Andrew Howroyd_, Sep 01 2019
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