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

%I A350881 #11 Mar 01 2022 07:25:03
%S A350881 1,2,4,10,24,50,140,368,1152,3682,11784,39902,134612,463066,1635092,
%T A350881 5818384,20684072,73693068,266943648,967762792,3533666568,13036452946,
%U A350881 48102671884,178315730764,661567489568,2450447537226,9123572154720,34201574126260
%N A350881 a(n) is the constant term in expansion of Product_{k=1..n} (x^prime(k) + 1/x^prime(k))^2.
%p A350881 p:= proc(n) option remember; `if`(n=0, 1,
%p A350881       p(n-1)*(x^ithprime(n)+1/x^ithprime(n))^2)
%p A350881     end:
%p A350881 a:= n-> coeff(p(n), x, 0):
%p A350881 seq(a(n), n=0..30);  # _Alois P. Heinz_, Jan 26 2022
%t A350881 p[n_] := p[n] = If[n == 0, 1, p[n - 1]*(x^Prime[n] + 1/x^Prime[n])^2];
%t A350881 a[n_] := Coefficient[p[n], x, 0];
%t A350881 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Mar 01 2022, after _Alois P. Heinz_ *)
%o A350881 (PARI) a(n) = polcoef (prod(k=1, n, (x^prime(k) + 1/x^prime(k))^2), 0); \\ _Michel Marcus_, Jan 21 2022
%Y A350881 Cf. A000980, A022894, A022896, A047653.
%K A350881 nonn
%O A350881 0,2
%A A350881 _Ilya Gutkovskiy_, Jan 20 2022