A006041 a(n+1) = (n^2 - 1)*a(n) + n + 1. (Formerly M1949)

0, 2, 9, 76, 1145, 27486, 962017, 46176824, 2909139921, 232731193690, 23040388175321, 2764846581038532, 395373061088510089, 66422674262869694966, 12952421481259590518385, 2901342411802148276118256, 739842315009547810410155297, 213074586722749769398124725554, 68823091511448175515594286353961

Offset

1,2

References

R. K. Guy, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

G. C. Greubel, Table of n, a(n) for n = 1..250

R. K. Guy, Letter to N. J. A. Sloane with attachment, Jun. 1991

Index entries for sequences related to Bessel functions or polynomials

Formula

Nearest integer to BesselI(1, 2)*(n-1)!*(n-1)!*n/(n-1), n>2.

Mathematica

Join[{0, 2}, Table[Floor[BesselI[1, 2]*(n - 1)!*(n - 1)!*n/(n - 1)], {n, 3, 50}]] (* G. C. Greubel, Aug 16 2017 *)
RecurrenceTable[{a[1]==0, a[n+1]==(n^2-1)a[n]+n+1}, a, {n, 20}] (* Harvey P. Dale, May 16 2020 *)

Prog

(PARI) a(n) = if (n==1, 0, (n^2-2*n)*a(n-1) + n); \\ Michel Marcus, Aug 16 2017

Crossrefs

Sequence in context: A006059 A277406 A182947 * A192551 A121131 A166891

Adjacent sequences: A006038 A006039 A006040 * A006042 A006043 A006044

Keyword

nonn,easy

Author

N. J. A. Sloane, Simon Plouffe

Extensions

More terms from James A. Sellers, May 01 2000

Status

approved