A002020 a(n+1) = a(n) - n*(n-1)*a(n-1), with a(n) = 1 for n <= 3.

1, 1, 1, 1, -5, -17, 83, 593, -2893, -36101, 172195, 3421285, -15520165, -467129785, 1954015955, 86971636825, -323371713725, -21196564551725, 66760541581475, 6552909294409325, -16279195926455125, -2506384727801998625, 4330877561309153875

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

References

• R. Kelisky, The numbers generated by exp(arctan x), Duke Math. J., 26 (1959), 569-581.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..100

Programs

Maple

f := proc(n) option remember; if n<=3 then 1 else f(n-1)-(n-1)*(n-2)*f(n-2); fi; end;

Mathematica

t = {1, 1, 1, 1}; Do[AppendTo[t, t[[-1]] - (n-1) (n - 2) t[[-2]]], {n, 4, 20}] (* T. D. Noe, Aug 30 2012 *)