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

30, 247, 1358, 5102, 16186, 41817, 98190, 220628, 441410, 852887, 1551568, 2631642, 4293186, 6866813, 10757450, 16151192, 23873746, 34440605, 48249066, 66877582, 91117898, 122953643, 165196270, 218615372, 284119458, 364962773, 462059210, 579605426, 732954370

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Programs

Maple

SymmPolyn := proc(L::list,n::integer)
    local c,a,sel;
    a :=0 ;
    sel := combinat[choose](nops(L),n) ;
    for c in sel do
        a := a+mul(L[e],e=c) ;
    end do:
    a;
end proc:
A024448 := proc(n)
    [seq(ithprime(k),k=1..n+2)] ;
    SymmPolyn(%,3) ;
end proc: # R. J. Mathar, Sep 23 2016
# second Maple program:
b:= proc(n) option remember; convert(series(`if`(n=0, 1,
      b(n-1)*(ithprime(n)*x+1)), x, 4), polynom)
    end:
a:= n-> coeff(b(n+2), x, 3):
seq(a(n), n=1..30);  # Alois P. Heinz, Sep 06 2019

Mathematica

b[n_] := b[n] = If[n == 0, 1, b[n - 1] (Prime[n] x + 1)];
a[n_] := SeriesCoefficient[b[n + 2], {x, 0, 3}];
a /@ Range[30] (* Jean-François Alcover, Feb 03 2020, after Alois P. Heinz *)