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A285382 Sum of entries in the last cycles of all permutations of [n].

%I A285382 #50 May 05 2017 10:53:56
%S A285382 1,5,25,143,942,7074,59832,563688,5858640,66622320,823055040,
%T A285382 10979133120,157300375680,2409321801600,39290164300800,
%U A285382 679701862425600,12433400027596800,239791474805299200,4863054420016128000,103462238924835840000,2304147629440419840000
%N A285382 Sum of entries in the last cycles of all permutations of [n].
%C A285382 Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
%H A285382 Alois P. Heinz, <a href="/A285382/b285382.txt">Table of n, a(n) for n = 1..449</a>
%H A285382 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A285382 Recursion: see Maple program.
%e A285382 a(3) = 25 because the sum of the entries in the last cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 6+6+3+2+5+3 = 25.
%p A285382 a:= proc(n) option remember; `if`(n<3, n*(3*n-1)/2,
%p A285382      ((2*n^2+3*n-1)*a(n-1)-(n+2)*(n-1)*n*a(n-2))/(n+1))
%p A285382     end:
%p A285382 seq(a(n), n=1..25);
%t A285382 Table[n! * (n-1 + 2*(n+1)*HarmonicNumber[n])/4, {n, 1, 25}] (* _Vaclav Kotesovec_, Apr 29 2017 *)
%Y A285382 Cf. A284816, A285424, A285439.
%Y A285382 Column k=1 of A286231.
%K A285382 nonn
%O A285382 1,2
%A A285382 _Alois P. Heinz_, Apr 20 2017