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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
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.
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
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 A338182 A135164
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, Apr 10 2018
STATUS
approved