A188914 a(n) = n*n! + 1 = (n+1)! - n! + 1.

1, 2, 5, 19, 97, 601, 4321, 35281, 322561, 3265921, 36288001, 439084801, 5748019201, 80951270401, 1220496076801, 19615115520001, 334764638208001, 6046686277632001, 115242726703104001, 2311256907767808001, 48658040163532800001, 1072909785605898240001

Offset: 0

Author

John M. Campbell, Apr 17 2011

Keywords

• nonn
• easy
• nice

Comments

It is unknown if all numbers of the form n*n!+1 are squarefree. n*n!+1 is squarefree for 0 < n < 52. It is unknown if there exist infinitely many primes of the form n*n!+1. For primes in this sequence, see A049984.

Crossrefs

Cf. A001563, A049984, A094258.

Programs

Mathematica

Table[(n*Factorial[n])+1,{n,0,30}]

PARI

a(n) = n*n! + 1; \\ Michel Marcus, Aug 03 2022

Formula

E.g.f.: exp(x) + x/(1 - x)^2. - Stefano Spezia, Aug 03 2022

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 03 2022