A176304 a(n) = (-1)^n * n * a(n-1) - 1, with a(0)=0.

0, -1, -3, 8, 31, -156, -937, 6558, 52463, -472168, -4721681, 51938490, 623261879, -8102404428, -113433661993, 1701504929894, 27224078878303, -462809340931152, -8330568136760737, 158280794598454002

Offset: 0

Author

Roger L. Bagula, Apr 14 2010

Keywords

• sign
• easy

Comments

The sequence alternates in the sign and in the odd-even parity.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445

Programs

Magma

function a(n)
  if n eq 0 then return 0;
  else return (-1)^n*n*a(n-1) -1;
  end if; return a; end function;
[a(n): n in [0..20]]; // G. C. Greubel, Nov 26 2019

Maple

a(n):=`if`(n=0, 0, (-1)^n*n*a(n-1) -1); seq(a(n), n=0..20); # G. C. Greubel, Nov 26 2019

Mathematica

a[n_]:= a[n] = If[n==0, 0, (-1)^n*n*a[n-1] -1]; Table[a[n], {n, 0, 20}]

PARI

a(n) = if(n==0, 0, (-1)^n*n*a(n-1) -1); \\ G. C. Greubel, Nov 26 2019

Sage

@CachedFunction
def a(n):
    if (n==0): return 0
    else: return (-1)^n*n*a(n-1) -1
[a(n) for n in (0..20)] # G. C. Greubel, Nov 26 2019