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%I #11 Jul 25 2018 15:01:27
%S 1,1,3,120,151200,10897286400,70959641905152000,
%T 60493719168990845337600000,9226024969987629401488081551360000000,
%U 329646772667218349211759153151614073700352000000000,3498788402132461399351052923160966975192989707740695756800000000000
%N Number of permutations on [n*(n+1)/2] with cycles of n distinct lengths.
%H Alois P. Heinz, <a href="/A246292/b246292.txt">Table of n, a(n) for n = 0..30</a>
%F a(n) = C(n+1,2)! / n!.
%F a(n) = A218868(n*(n+1)/2,n) = A218868(A000217(n),n).
%F a(n) = A242027(n*(n+1)/2,n) = A242027(A000217(n),n).
%F a(n) = A022915(n) * A000178(n-1) for n>0.
%p a:= n-> binomial(n+1, 2)!/n!:
%p seq(a(n), n=0..12);
%Y Cf. A000142, A000178, A000217, A022915, A218868, A242027, A317165.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 21 2014
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