A300559 a(n) = n*(n+1)!/2 + 1.

1, 2, 7, 37, 241, 1801, 15121, 141121, 1451521, 16329601, 199584001, 2634508801, 37362124801, 566658892801, 9153720576001, 156920924160001, 2845499424768001, 54420176498688001, 1094805903679488001, 23112569077678080001, 510909421717094400001, 11802007641664880640001

Offset: 0

Author

M. F. Hasler, Apr 10 2018

Keywords

• nonn
• easy

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.

Crossrefs

Inspired by A302859.

Cf. A301373.

Programs

Magma

[n*Factorial(n+1)/2+1: n in [0..25]]; // Vincenzo Librandi, Apr 12 2018

Mathematica

Array[# (# + 1)!/2 + 1 &, 22, 0] (* Michael De Vlieger, Apr 10 2018 *)

PARI

apply( A300559=n->(n+1)!\2*n+1, [0..25])

Formula

a(n) = A180119(n) + 1 = A001286(n+1) + 1.

D-finite with recurrence 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