A369390 a(n) = [x^prime(n)] Product_{k=1..n} (x^prime(k) + 1 + 1/x^prime(k)).

1, 1, 2, 4, 6, 13, 31, 77, 188, 449, 1191, 3014, 7920, 21498, 57833, 154073, 412733, 1141274, 3106771, 8576977, 24015471, 66489615, 185886699, 517837152, 1435964205, 4034697191, 11438332340, 32395341851, 92396549863, 263233759500, 736127855014, 2093027604453

Offset: 1

Author

Ilya Gutkovskiy, Jan 22 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..400

Crossrefs

Cf. A063890, A316706, A350880.

Programs

Maple

s:= proc(n) s(n):= `if`(n<1, 0, ithprime(n)+s(n-1)) end:
b:= proc(n, i) option remember; `if`(n>s(i), 0, `if`(i=0, 1,
      b(n, i-1)+b(n+ithprime(i), i-1)+b(abs(n-ithprime(i)), i-1)))
    end:
a:= n-> b(ithprime(n), n):
seq(a(n), n=1..40);  # Alois P. Heinz, Jan 22 2024

Mathematica

Table[Coefficient[Product[(x^Prime[k] + 1 + 1/x^Prime[k]), {k, 1, n}], x, Prime[n]], {n, 1, 32}]