A356684 a(n) = (n-1)*a(n-1) - n*a(n-2), with a(1) = a(2) = -1.

-1, -1, 1, 7, 23, 73, 277, 1355, 8347, 61573, 523913, 5024167, 53479135, 624890417, 7946278813, 109195935523, 1612048228547, 25439293045885, 427278358483537, 7609502950269503, 143217213477235783, 2840152418116022377

Offset: 1

Author

Mohammed Bouras, Aug 22 2022

Keywords

• sign
• easy

Links

• Mohammed Bouras, A new sequence of prime numbers, Romanian Math. Mag. (15 August 2022). See Table 1 p. 1.
• Mohammed Bouras, A New Sequence of Prime Numbers, EasyChair Preprint 8686, 2022.

Crossrefs

Cf. A051403, A356247.

Programs

Mathematica

a[1]=a[2]=-1; a[n_]:=a[n]=(n-1)a[n-1]-n a[n-2]; Array[a,22] (* Stefano Spezia, Aug 23 2022 *)

PARI

a(n) = if(n<=2, -1, 1/2*((n-1)*sum(k=0,n-3,k!) + n*(n-2)*sum(k=0,n-4,k!))) \\ Jianing Song, Oct 15 2022, following the formula above

Formula

a(n) = A051403(n-3) + n*A051403(n-4).

a(n)/(n^2 - n - 1) = 1/(2-3/(3-4/(4-5/(...(n-1)-n/(n-(n+1)))))), for n >= 2.