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A024448 a(n) = 3rd elementary symmetric function of the first n+2 primes.

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