A224869 a(n) = n*( a(n-1)+1 ), initialized by a(1) = -1.

-1, 0, 3, 16, 85, 516, 3619, 28960, 260649, 2606500, 28671511, 344058144, 4472755885, 62618582404, 939278736075, 15028459777216, 255483816212689, 4598708691828420, 87375465144739999, 1747509302894800000, 36697695360790800021, 807349297937397600484

Offset: 1

Author

Alex Ratushnyak, Jul 22 2013

Keywords

• sign
• easy

Examples

			a(4) = 4*(a(3)+1) = 4*4 = 16.
		

Crossrefs

Cf. A007526, A038156, A166554, A121662 (3rd column).

Programs

Mathematica

A224869[1] := -1; A224869[n_] := A224869[n - 1]n + n; Table[A224869[n], {n, 40}] (* Alonso del Arte, Jul 22 2013 *)

Python

a=-1
for n in range(2,24):
  print(a, end=', ')
  a= n*(a+1)

Formula

a(n) +(-n-2)*a(n-1) +(2*n-1)*a(n-2) +(-n+2)*a(n-3)=0. - R. J. Mathar, Jul 28 2013

a(n) = exp(1)*n*Gamma(n,1) - 2*Gamma(n+1,0). - Martin Clever, Mar 27 2023