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%I M1949 #25 May 16 2020 14:36:59
%S 0,2,9,76,1145,27486,962017,46176824,2909139921,232731193690,
%T 23040388175321,2764846581038532,395373061088510089,
%U 66422674262869694966,12952421481259590518385,2901342411802148276118256,739842315009547810410155297,213074586722749769398124725554,68823091511448175515594286353961
%N a(n+1) = (n^2 - 1)*a(n) + n + 1.
%D R. K. Guy, personal communication.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. C. Greubel, <a href="/A006041/b006041.txt">Table of n, a(n) for n = 1..250</a>
%H R. K. Guy, <a href="/A001599/a001599_1.pdf">Letter to N. J. A. Sloane with attachment, Jun. 1991</a>
%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F Nearest integer to BesselI(1, 2)*(n-1)!*(n-1)!*n/(n-1), n>2.
%t Join[{0, 2}, Table[Floor[BesselI[1, 2]*(n - 1)!*(n - 1)!*n/(n - 1)], {n, 3, 50}]] (* _G. C. Greubel_, Aug 16 2017 *)
%t RecurrenceTable[{a[1]==0,a[n+1]==(n^2-1)a[n]+n+1},a,{n,20}] (* _Harvey P. Dale_, May 16 2020 *)
%o (PARI) a(n) = if (n==1, 0, (n^2-2*n)*a(n-1) + n); \\ _Michel Marcus_, Aug 16 2017
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from _James A. Sellers_, May 01 2000
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