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%I #10 Jul 18 2023 16:11:29
%S 1,5,16,64,298,1540,8506,48844,286498,1699300,10136746,60643324,
%T 363328498,2178376660,13065476986,78378513004,470228031298,
%U 2821239047620,16927046865226,101561118929884,609363226794898,3656168900416180,21936982021437466,131621797985445964
%N Number of set partitions of [3*n] such that within each block the numbers of elements from all residue classes modulo n are equal for n>0, a(0)=1.
%H Alois P. Heinz, <a href="/A275100/b275100.txt">Table of n, a(n) for n = 0..1000</a>
%H J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/SIXDENIERS/bell.html">Extended Bell and Stirling Numbers From Hypergeometric Exponentiation</a>, J. Integer Seqs. Vol. 4 (2001), #01.1.4.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-27,18).
%F G.f.: -(21*x^3-7*x^2-5*x+1)/((x-1)*(6*x-1)*(3*x-1)).
%t CoefficientList[Series[-(21x^3-7x^2-5x+1)/((x-1)(6x-1)(3x-1)),{x,0,30}],x] (* _Harvey P. Dale_, Dec 15 2018 *)
%Y Row n=3 of A275043.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Jul 16 2016
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