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%I #9 Sep 20 2019 13:12:11
%S 1,1,3,12,67,465,3675,30024,299250,3417690,38983966,446295630,
%T 6494597538,95113861987,1365645758568,20909896016688,373941213111567,
%U 6583031224561656,114432377809889706,2158725804226303597,45003872172663258463,928103099363098553160
%N The maximal number of partitions of {1..3n} that are invariant under a permutation consisting of n 3-cycles, and which have the same number of nonempty parts.
%H Andrew Howroyd, <a href="/A294202/b294202.txt">Table of n, a(n) for n = 0..200</a>
%o (PARI)
%o G(n)={Vec(serlaplace(exp(sumdiv(3, d, y^d*(exp(d*x + O(x*x^n))-1)/d))))}
%o seq(n)={my(A=G(n)); vector(#A, n, vecmax(Vec(A[n])))} \\ _Andrew Howroyd_, Sep 20 2019
%Y Maximum row values of A294201.
%Y Cf. A002873.
%K nonn
%O 0,3
%A _Andrew Howroyd_, Oct 24 2017
%E a(0)=1 prepended by _Andrew Howroyd_, Sep 20 2019
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