%I #12 Feb 03 2020 10:35:04
%S 30,247,1358,5102,16186,41817,98190,220628,441410,852887,1551568,
%T 2631642,4293186,6866813,10757450,16151192,23873746,34440605,48249066,
%U 66877582,91117898,122953643,165196270,218615372,284119458,364962773,462059210,579605426,732954370
%N a(n) = 3rd elementary symmetric function of the first n+2 primes.
%H Alois P. Heinz, <a href="/A024448/b024448.txt">Table of n, a(n) for n = 1..10000</a>
%p SymmPolyn := proc(L::list,n::integer)
%p local c,a,sel;
%p a :=0 ;
%p sel := combinat[choose](nops(L),n) ;
%p for c in sel do
%p a := a+mul(L[e],e=c) ;
%p end do:
%p a;
%p end proc:
%p A024448 := proc(n)
%p [seq(ithprime(k),k=1..n+2)] ;
%p SymmPolyn(%,3) ;
%p end proc: # _R. J. Mathar_, Sep 23 2016
%p # second Maple program:
%p b:= proc(n) option remember; convert(series(`if`(n=0, 1,
%p b(n-1)*(ithprime(n)*x+1)), x, 4), polynom)
%p end:
%p a:= n-> coeff(b(n+2), x, 3):
%p seq(a(n), n=1..30); # _Alois P. Heinz_, Sep 06 2019
%t b[n_] := b[n] = If[n == 0, 1, b[n - 1] (Prime[n] x + 1)];
%t a[n_] := SeriesCoefficient[b[n + 2], {x, 0, 3}];
%t a /@ Range[30] (* _Jean-François Alcover_, Feb 03 2020, after _Alois P. Heinz_ *)
%K nonn
%O 1,1
%A _Clark Kimberling_