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 A075840 Primes of the form (2*n)!/(n!)^2+1. 2
 2, 3, 7, 71, 3433, 2704157, 35345263801, 2104098963721, 6892620648693261354601, 410795449442059149332177041, 1520803477811874490019821888415218657, 5949105755928259715106809205795376486501, 1480212998448786189993816895482588794876101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES New Zealand Science Monthly, Bulletin Board, Feb. 1999. Binomial(300,150)+185 = nextprime. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..25 EXAMPLE 7 is a term because C(4,2)+1 = 6+1 = 7 is prime. MATHEMATICA a = Select[ Range[100], PrimeQ[Binomial[2#, # ] + 1] & ]; Binomial[2a, a] + 1 Select[Table[(2 n)! / (n!)^2 + 1, {n, 0, 80}], PrimeQ] (* Vincenzo Librandi, Mar 17 2015 *) PROG (PARI) v=[]; for(n=0, 100, x=bin(2*n, n)+1; if(isprime(x), v=concat(v, x), )); v (MAGMA) [a: n in [0..100] | IsPrime(a) where a is Factorial(2*n) div Factorial(n)^2+1]; // Vincenzo Librandi Mar 17 2015 CROSSREFS Cf. A092751 = n such that (2*n)!/(n!)^2+1 is prime, A112858 = primes of the form (2*n)!/(n!)^2-1. Cf. A000984, n's are in A066699. Sequence in context: A130309 A090870 A088542 * A096225 A035094 A084729 Adjacent sequences:  A075837 A075838 A075839 * A075841 A075842 A075843 KEYWORD nonn AUTHOR Donald S. McDonald, Oct 14 2002 EXTENSIONS Edited by Robert G. Wilson v, Oct 15 2002 Definition corrected by Alexander Adamchuk, Nov 30 2007 Edited by N. J. A. Sloane, Nov 30 2007 a(13) from Vincenzo Librandi, Mar 17 2015 STATUS approved

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Last modified December 11 07:35 EST 2019. Contains 329914 sequences. (Running on oeis4.)