cp's OEIS Frontend

A285489 Sum of entries in the second cycles of all permutations of [n].

%I A285489 #14 Jun 01 2018 16:39:32
%S A285489 2,12,76,545,4422,40194,405072,4484808,54121680,707105520,9944043840,
%T A285489 149769846720,2405254884480,41029304803200,740857462732800,
%U A285489 14117363667993600,283111532808652800,5960312380873267200,131434781395405824000,3029635129259289600000
%N A285489 Sum of entries in the second cycles of all permutations of [n].
%H A285489 Alois P. Heinz, <a href="/A285489/b285489.txt">Table of n, a(n) for n = 2..448</a>
%H A285489 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A285489 Recursion: see Maple program.
%F A285489 E.g.f.: x*(x*(x-2)+2*(x-1)^2*log(1-x))/(4*(x-1)^3).
%F A285489 a(n) ~ n! * n^2 / 8. - _Vaclav Kotesovec_, Apr 20 2017
%e A285489 a(3) = 12 because the sum of the entries in the second cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 0+0+3+2+5+2 = 12.
%p A285489 a:= proc(n) option remember; `if`(n<3, (n-1)*n,
%p A285489       ((2*n^3-7*n^2+11*n-8)*n*a(n-1)-(n-1)*(n-2)
%p A285489       *(n^2-n+2)*n*a(n-2))/((n^2-3*n+4)*(n-1)))
%p A285489     end:
%p A285489 seq(a(n), n=2..25);
%t A285489 a[2] = 2; a[3] = 12; a[n_] := a[n] = ((2n^3 - 7n^2 + 11n - 8) n a[n-1] - (n-1)(n-2)(n^2 - n + 2) n a[n-2])/((n^2 - 3n + 4)(n-1));
%t A285489 Table[a[n], {n, 2, 25}] (* _Jean-François Alcover_, Jun 01 2018, from Maple *)
%Y A285489 Column k=2 of A285439.
%K A285489 nonn
%O A285489 2,1
%A A285489 _Alois P. Heinz_, Apr 19 2017