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%I #12 Dec 30 2023 16:26:17
%S 1,1,1,3,2,5,3,7,4,9,5,11,6,143,7,15,104,935,9,19,10,21,11,4025,3900,
%T 325,3289,27,14,29,15,31,368,33,17,35,18,185,19,39,380,451,399,215,
%U 770,45,23,29563,24,12397,725,51,26,1537,837,2365,1036,285,377,2537,30
%N Product_{i=1..n} i^i / denominator( Sum_{j=1..n} j(j+1)/2 / (Product_{k=0..i-1} j!/k!) ).
%C Most of the time a(2n-1)=2n-1, but a(2n-1)!=2n-1 for 2n-1 = 13,17,23,25,37,41,43,47,49,53,55,57,59,61,63,...
%C Most of the time a(2n)=n, but a(2n)!=n for 2n = 16,24,26,32,40,42,44,50,54,56,58,64,84,86,96,100,102,104,...
%e a(3) = 108/36 = 3.
%t f[n_] := Product[k^k, {k, 1, n}]/ Denominator[Sum[i(i + 1)/2/Product[i!/j!, {j, 0, i - 1}], {i, n}]]; Table[ f[n], {n, 0, 61}] (* _Robert G. Wilson v_, Apr 18 2005 *)
%Y Cf. A002109 - hyperfactorial numbers.
%K nonn
%O 0,4
%A Jess E. Boling (tdbpeekitup(AT)yahoo.com), Apr 17 2005
%E Edited by _Robert G. Wilson v_, Apr 18 2005
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