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A286175 Sum of the n-th entries in all cycles of all permutations of [n+1]. 2
4, 13, 43, 192, 1068, 7080, 54360, 473760, 4616640, 49714560, 586051200, 7504358400, 103703846400, 1538074137600, 24366332390400, 410609751552000, 7333437855744000, 138362409529344000, 2749819506610176000, 57416487392968704000, 1256593887223234560000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..448

FORMULA

E.g.f.: -2*log(1-x)-(5*x^3-10*x^2+10*x-7)/(2*(1-x)^2)-7/2.

a(n) = A285793(n+1,n).

EXAMPLE

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.

MAPLE

a:= proc(n) option remember; `if`(n<3, [4, 13][n],

      (n-1)*(2*n^2+7*n+4)*a(n-1)/(2*n^2+3*n-1))

    end:

seq(a(n), n=1..25);

CROSSREFS

Cf. A285793.

Sequence in context: A113986 A149426 A042767 * A252831 A219708 A345230

Adjacent sequences:  A286172 A286173 A286174 * A286176 A286177 A286178

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 03 2017

STATUS

approved

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Last modified September 22 21:04 EDT 2021. Contains 347608 sequences. (Running on oeis4.)