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Multinomial coefficient (2+3+...+prime(n); 2,3,5,7,...,prime(n)) = A007504(n)! / A111180(n).
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%I #11 Nov 04 2014 23:09:16

%S 1,10,2520,49008960,1052427228652800,18543848132205515927808000,

%T 3663312848979081767807855264321333760000,

%U 1860046674511129497317809046448809961990598435124736000000,46250563343969315569958487234182581699417368835772148395100189090556723200000000

%N Multinomial coefficient (2+3+...+prime(n); 2,3,5,7,...,prime(n)) = A007504(n)! / A111180(n).

%p a := n -> add(ithprime(k),k=1..n)!/mul(ithprime(k)!,k=1..n);

%p seq(a(n),n=0..9); # _Peter Luschny_, Nov 04 2014

%o (PARI) a(n) = my(d=1,t=0); forprime(p=2,prime(n),d*=p!;t+=p);t!\d

%Y Cf. A000040, A007504, A111180, A022915

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, Nov 03 2014