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A285795 Sum of the second entries in all cycles of all permutations of [n].

%I A285795 #11 May 03 2017 12:38:35
%S A285795 0,0,2,13,83,582,4554,39672,382248,4044240,46663920,583554240,
%T A285795 7865622720,113711230080,1755484617600,28828769356800,501858148377600,
%U A285795 9232213174732800,178968924600883200,3646603415927808000,77916767838981120000,1742147265551616000000
%N A285795 Sum of the second entries in all cycles of all permutations of [n].
%C A285795 Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
%H A285795 Alois P. Heinz, <a href="/A285795/b285795.txt">Table of n, a(n) for n = 0..449</a>
%H A285795 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%e A285795 a(3) = 13 because the sum of the second entries in all cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 2+3+2+3+3+0 = 13.
%p A285795 a:= proc(n) option remember; `if`(n<3, n*(n-1),
%p A285795      ((2*n^2+3*n-1)*a(n-1)-(n-1)*n*(n+2)*a(n-2))/(n+1))
%p A285795     end:
%p A285795 seq(a(n), n=0..25);
%t A285795 Flatten[{0, Table[n! * (2*(n+1)*HarmonicNumber[n] - n - 3)/4, {n, 1, 25}]}] (* _Vaclav Kotesovec_, Apr 29 2017 *)
%Y A285795 Column k=2 of A285793.
%Y A285795 Cf. A001008, A002805.
%K A285795 nonn
%O A285795 0,3
%A A285795 _Alois P. Heinz_, Apr 26 2017