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%I #6 Jul 15 2016 15:34:44
%S 1,1,1,1,2,4,8,20,50,125,375,1125,3375,11700,40560,140608,548912,
%T 2142868,8365427,36140293,156133187,674526133,3184194060,15031429200,
%U 70957944000,362451121200,1851389821260,9456845543523,51863510753775,284431392616875
%N Number of set partitions of [n] such that i-j is a multiple of three for all i,j belonging to the same block.
%H Alois P. Heinz, <a href="/A275070/b275070.txt">Table of n, a(n) for n = 0..699</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F a(n) = Product_{i=0..2} A000110(floor((n+i)/3)).
%e a(7) = 20: 147|25|36, 14|25|36|7, 147|25|3|6, 14|25|3|6|7, 147|2|36|5, 14|2|36|5|7, 147|2|3|5|6, 14|2|3|5|6|7, 17|25|36|4, 1|25|36|47, 1|25|36|4|7, 17|25|3|4|6, 1|25|3|47|6, 1|25|3|4|6|7, 17|2|36|4|5, 1|2|36|47|5, 1|2|36|4|5|7, 17|2|3|4|5|6, 1|2|3|47|5|6, 1|2|3|4|5|6|7.
%Y Column k=3 of A275069.
%Y Cf. A000110.
%K nonn
%O 0,5
%A _Alois P. Heinz_, Jul 15 2016
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