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A286175 Sum of the n-th entries in all cycles of all permutations of [n+1].

%I A286175 #10 Apr 21 2022 05:23:39
%S A286175 4,13,43,192,1068,7080,54360,473760,4616640,49714560,586051200,
%T A286175 7504358400,103703846400,1538074137600,24366332390400,410609751552000,
%U A286175 7333437855744000,138362409529344000,2749819506610176000,57416487392968704000,1256593887223234560000
%N A286175 Sum of the n-th entries in all cycles of all permutations of [n+1].
%H A286175 Alois P. Heinz, <a href="/A286175/b286175.txt">Table of n, a(n) for n = 1..448</a>
%F A286175 E.g.f.: -2*log(1-x)-(5*x^3-10*x^2+10*x-7)/(2*(1-x)^2)-7/2.
%F A286175 a(n) = A285793(n+1,n).
%e A286175 a(2) = 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 A286175 a:= proc(n) option remember; `if`(n<3, [4, 13][n],
%p A286175       (n-1)*(2*n^2+7*n+4)*a(n-1)/(2*n^2+3*n-1))
%p A286175     end:
%p A286175 seq(a(n), n=1..25);
%t A286175 a[n_] := a[n] = If[n < 3, {4, 13}[[n]],
%t A286175      (n-1)*(2*n^2 + 7*n + 4)*a[n-1]/(2*n^2 + 3*n - 1)];
%t A286175 Table[a[n], {n, 1, 25}] (* _Jean-François Alcover_, Apr 21 2022, after _Alois P. Heinz_ *)
%Y A286175 Cf. A285793.
%K A286175 nonn
%O A286175 1,1
%A A286175 _Alois P. Heinz_, May 03 2017