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a(n) = (n+1)(n+2)...(n+prime(k)) where prime(k) <= n < prime(k+1).
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%I #15 Jul 20 2020 02:27:00

%S 12,120,210,30240,55440,17297280,32432400,57657600,98017920,

%T 28158588057600,53970627110400,64764752532480000,124903451312640000,

%U 233153109116928000,422590010274432000,830034394580628357120000

%N a(n) = (n+1)(n+2)...(n+prime(k)) where prime(k) <= n < prime(k+1).

%H Robert Israel, <a href="/A110423/b110423.txt">Table of n, a(n) for n = 2..366</a>

%F a(p) = (2p)!/p! if p is a prime.

%F a(n) = (n+A007917(n))!/n!. - _Robert Israel_, Aug 18 2019

%e a(6) = 7*8*9*10*11 = 55440.

%p p:=proc(n) if isprime(n)=true then n else prevprime(n) fi end: a:=n->product(n+j,j=1..p(n)): seq(a(n),n=2..19); # p is a modified prevprime command (for n prime yields n rather than the previous prime) # _Emeric Deutsch_, Aug 07 2005

%p # Simpler alternative:

%p seq((n+prevprime(n+1))!/n!, n=2..20);# _Robert Israel_, Aug 18 2019

%t Table[Pochhammer[n+1, NextPrime[n+1, -1]], {n, 2, 20}] (* _Jean-François Alcover_, Jul 19 2020 *)

%Y Cf. A007917, A110424.

%K easy,nonn

%O 2,1

%A _Amarnath Murthy_, Aug 01 2005

%E More terms from _Emeric Deutsch_, Aug 07 2005