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A024448 a(n) = 3rd elementary symmetric function of the first n+2 primes. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

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-Fran├žois Alcover, Feb 03 2020, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A042752 A334981 A230703 * A125367 A126525 A230615

Adjacent sequences:  A024445 A024446 A024447 * A024449 A024450 A024451

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified October 26 14:28 EDT 2021. Contains 348267 sequences. (Running on oeis4.)