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%I #18 Dec 12 2023 13:45:11
%S 1,1,1,2,2,2,3,3,3,4,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,11,
%T 11,11,12,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,18,18,
%U 18,19,19,19,20,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24
%N a(n) is the value d<n/2 maximizing the expression d!*(d + 1)!*2^(n-2*d-1)*stirling2(n-d, d+1), for n>=4.
%C In case the maximum should turn out not to be unique, use the smallest value. - _N. J. A. Sloane_, Apr 22 2017
%H Robert Davis, Sarah A. Nelson, T. Kyle Petersen, Bridget E. Tenner, <a href="https://arxiv.org/abs/1704.05494">The pinnacle set of a permutation</a>, arXiv:1704.05494 [math.CO], 2017.
%p f:= n -> max[index]([seq(d!*(d+1)!*2^(n-2*d-1)*Stirling2(n-d,d+1), d=1..n/2)]):
%p map(f, [$4..200]); # _Robert Israel_, Apr 20 2017
%t a[n_] := MaximalBy[Table[{d, d! (d+1)! 2^(n-2d-1) StirlingS2[n-d, d+1]}, {d, 1, n/2}], Last][[All, 1]] // Min;
%t Table[a[n], {n, 4, 78}] (* _Jean-François Alcover_, Sep 18 2018 *)
%o (PARI) half(n) = if (n % 2, n\2, n/2 - 1);
%o a(n) = {v = vector(half(n), d, d!*(d + 1)!*(2^(n-2*d-1)*stirling(n-d, d+1, 2))); w = vecsort(v,,1); w[#w];}
%Y Cf. A285525, A285526.
%K nonn
%O 4,4
%A _Michel Marcus_, Apr 20 2017
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