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%I #58 Mar 19 2024 03:27:37
%S 1,2,7,37,241,1801,15121,141121,1451521,16329601,199584001,2634508801,
%T 37362124801,566658892801,9153720576001,156920924160001,
%U 2845499424768001,54420176498688001,1094805903679488001,23112569077678080001,510909421717094400001,11802007641664880640001
%N a(n) = n*(n+1)!/2 + 1.
%C See A301373 and A302859 for the primes: it is remarkable that all of a(1..10) are primes, and only a(11) is the first composite term.
%H Maheswara Rao Valluri, <a href="https://arxiv.org/abs/1803.11461">Primes of the form p = 1 + n! Sum n, for some n ∈ N*</a>, arXiv:1803.11461 [math.GM], 2018.
%H Simon Plouffe, <a href="http://vixra.org/abs/1409.0048">Conjectures of the OEIS, as of June 20, 2018.</a>
%F a(n) = A180119(n) + 1 = A001286(n+1) + 1.
%F D-finite with recurrence n*a(n+1) = (n+1)*(n+2)*(a(n)-1) + n. - _Chai Wah Wu_, Apr 11 2018
%F E.g.f.: exp(x)-1/(x-1)^3*x. - _Simon Plouffe_, Jun 21 2018
%t Array[# (# + 1)!/2 + 1 &, 22, 0] (* _Michael De Vlieger_, Apr 10 2018 *)
%o (PARI) apply( A300559=n->(n+1)!\2*n+1, [0..25])
%o (Magma) [n*Factorial(n+1)/2+1: n in [0..25]]; // _Vincenzo Librandi_, Apr 12 2018
%Y Inspired by A302859.
%Y Cf. A301373.
%K nonn,easy
%O 0,2
%A _M. F. Hasler_, Apr 10 2018
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