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%I #35 Jul 16 2015 22:09:22
%S 1,2,15,1,593775,1,1985871372366807082113118777430351536,1,1,1
%N C(n#, (n-1)#), where n# is the primorial A034386(n), the product of primes <= n.
%C Next term a(11) has 305 digits.
%C a(n) = 1 if and only if n is nonprime. When n is composite, n# and (n-1)# are the same, and since C(n, n) = 1, a(n) = 1 as well.
%F a(n) = binomial(n#, (n-1)#).
%F a(n) = n^A010051(n)*binomial(n# - 1, (n-1)# - 1). - _Arkadiusz Wesolowski_, Oct 21 2013
%e a(3) = 15 because the 3rd primorial is 6, the (3-1)th primorial is 2, and C(6, 2) = 15.
%e a(5) = (product_{i=5#-3#+1..5#} a(i))/(3#)! = 25*26*27*28*29*30/6! = 593775.
%t lst = {}; Do[AppendTo[lst, Binomial[Product[Prime[i], {i, n}], Product[Prime[i], {i, n - 1}]]]; AppendTo[lst, Table[1, {Prime[n + 1] - Prime[n] - 1}]], {n, 6}]; Prepend[Flatten[lst], 1]
%o (PARI) a(n)=my(k=prod(i=1,primepi(n),prime(i)));binomial(k,k/n) \\ _Charles R Greathouse IV_, Nov 30 2011
%Y Cf. A034386.
%K nonn
%O 1,2
%A _Arkadiusz Wesolowski_, Nov 26 2011
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