|
%I #13 Dec 26 2022 15:48:36
%S 2,11,41,118,316,693,1407,2528,4322,7251,11281,17238,25356,35633,
%T 48887,66324,88862,115763,149397,189796,236516,292843,358579,436454,
%U 529962,637123,756809,892164,1041712,1209065,1411503,1636954,1890678,2167149,2484221,2828048
%N a(n) = 2nd elementary symmetric function of {1, prime(1), prime(2), ..., prime(n-1)}, where prime(0) = 1.
%p b:= proc(n) option remember; convert(series(`if`(n=0, 1, b(n-1)*
%p (`if`(n=1, 1, ithprime(n-1))*x+1)), x, 3), polynom)
%p end:
%p a:= n-> coeff(b(n), x, 2):
%p seq(a(n), n=2..40); # _Alois P. Heinz_, Sep 08 2019
%t b[n_] := b[n] = Series[If[n == 0, 1, b[n - 1]*(If[n == 1, 1, Prime[n - 1]]*x + 1)], {x, 0, 3}] // Normal;
%t a[n_] := Coefficient[b[n], x, 2];
%t Table[a[n], {n, 2, 40}] (* _Jean-François Alcover_, Dec 26 2022, after _Alois P. Heinz_ *)
%Y Cf. A000040.
%K nonn
%O 2,1
%A _Clark Kimberling_
|
