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%I #25 Aug 03 2022 14:58:01
%S 1,2,5,19,97,601,4321,35281,322561,3265921,36288001,439084801,
%T 5748019201,80951270401,1220496076801,19615115520001,334764638208001,
%U 6046686277632001,115242726703104001,2311256907767808001,48658040163532800001,1072909785605898240001
%N a(n) = n*n! + 1 = (n+1)! - n! + 1.
%C 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.
%F E.g.f.: exp(x) + x/(1 - x)^2. - _Stefano Spezia_, Aug 03 2022
%t Table[(n*Factorial[n])+1,{n,0,30}]
%o (PARI) a(n) = n*n! + 1; \\ _Michel Marcus_, Aug 03 2022
%Y Cf. A001563, A049984, A094258.
%K nonn,easy,nice
%O 0,2
%A _John M. Campbell_, Apr 17 2011
%E a(0)=1 prepended by _Alois P. Heinz_, Aug 03 2022
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