A334716 a(n) = !n + n * n!, where !n = A000166(n) is subfactorial of n.

1, 1, 5, 20, 105, 644, 4585, 37134, 337393, 3399416, 37622961, 453769370, 5924234041, 83242063332, 1252567177849, 20096182035734, 342461702459745, 6177536369911664, 117598028364137953, 2356007639327453106, 49553054794725702121, 1091705092860949184540

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..448

Wikipedia, Derangement

Formula

E.g.f.: x/(x-1)^2 - exp(-x)/(x-1).

a(n) = A000166(n) + A001563(n) = !n + n * n!.

Maple

a:= proc(n) option remember; `if`(n<3, [1, 1, 5][n+1],
      ((2*n+1)*(n-1)*a(n-1)-(n-1)*(n^2-2*n-2)*a(n-2)
       -(n+1)*(n-1)*(n-2)*a(n-3))/n)
    end:
seq(a(n), n=0..23);

Mathematica

a[n_] := Subfactorial[n] + n n!;
a /@ Range[0, 23] (* Jean-François Alcover, Apr 26 2021 *)

Crossrefs

Main diagonal of A334715.

Cf. A000142, A000166, A001563.

Sequence in context: A259275 A109500 A137961 * A167145 A277032 A300490

Adjacent sequences: A334713 A334714 A334715 * A334717 A334718 A334719

Keyword

nonn

Author

Alois P. Heinz, May 08 2020

Status

approved