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 A300559 a(n) = n*(n+1)!/2 + 1. 3
 1, 2, 7, 37, 241, 1801, 15121, 141121, 1451521, 16329601, 199584001, 2634508801, 37362124801, 566658892801, 9153720576001, 156920924160001, 2845499424768001, 54420176498688001, 1094805903679488001, 23112569077678080001, 510909421717094400001, 11802007641664880640001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. LINKS Maheswara Rao Valluri, Primes of the form p = 1 + n! Sum n, for some n ∈ N*, arXiv:1803.11461 [math.GM], 2018. Simon Plouffe, Conjectures of the OEIS, as of June 20, 2018. FORMULA a(n) = A180119(n) + 1 = A001286(n+1) + 1. n*a(n+1) = (n+1)*(n+2)*(a(n)-1) + n. - Chai Wah Wu, Apr 11 2018 E.g.f.: exp(x)-1/(x-1)^3*x. - Simon Plouffe, Jun 21 2018 MAPLE seq(n*(n+1)!/2+1, n=0..21); # Paolo P. Lava, May 17 2018 MATHEMATICA Array[# (# + 1)!/2 + 1 &, 22, 0] (* Michael De Vlieger, Apr 10 2018 *) PROG (PARI) apply( A300559=n->(n+1)!\2*n+1, [0..25]) (MAGMA) [n*Factorial(n+1)/2+1: n in [0..25]]; // Vincenzo Librandi, Apr 12 2018 CROSSREFS Inspired by A302859. Cf. A301373. Sequence in context: A063766 A020040 A125191 * A302859 A135164 A321087 Adjacent sequences:  A300556 A300557 A300558 * A300560 A300561 A300562 KEYWORD nonn AUTHOR M. F. Hasler, Apr 10 2018 STATUS approved

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Last modified March 28 11:49 EDT 2020. Contains 333083 sequences. (Running on oeis4.)