A350881 a(n) is the constant term in expansion of Product_{k=1..n} (x^prime(k) + 1/x^prime(k))^2.

1, 2, 4, 10, 24, 50, 140, 368, 1152, 3682, 11784, 39902, 134612, 463066, 1635092, 5818384, 20684072, 73693068, 266943648, 967762792, 3533666568, 13036452946, 48102671884, 178315730764, 661567489568, 2450447537226, 9123572154720, 34201574126260

Offset: 0

Author

Ilya Gutkovskiy, Jan 20 2022

Keywords

• nonn

Crossrefs

Cf. A000980, A022894, A022896, A047653.

Programs

Maple

p:= proc(n) option remember; `if`(n=0, 1,
      p(n-1)*(x^ithprime(n)+1/x^ithprime(n))^2)
    end:
a:= n-> coeff(p(n), x, 0):
seq(a(n), n=0..30);  # Alois P. Heinz, Jan 26 2022

Mathematica

p[n_] := p[n] = If[n == 0, 1, p[n - 1]*(x^Prime[n] + 1/x^Prime[n])^2];
a[n_] := Coefficient[p[n], x, 0];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 01 2022, after Alois P. Heinz *)

PARI

a(n) = polcoef (prod(k=1, n, (x^prime(k) + 1/x^prime(k))^2), 0); \\ Michel Marcus, Jan 21 2022