A309803 a(n) is the coefficient of x^n in the polynomial Product_{i=1..n+3} (prime(i)*x-1).

-1, -17, -288, -5102, -107315, -2429223, -64002818, -2057205252, -69940351581, -2788890538777, -122099137635118, -5580021752377242, -276932659619923555, -15388458479166668283, -946625238259888348698, -60082571176666116692888, -4171440414742758122621945

Offset: 0

Author

Alexey V. Bazhin, Aug 17 2019

Keywords

• sign
• easy

Links

• Alexey V. Bazhin, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000040, A002110, A024451, A070918, A309802, A309804, A033999, A007504, A024447, A024448, A024449, A054640, A005867, A238146, A260613.

Programs

Maple

a:= n-> coeff(mul(ithprime(i)*x-1, i=1..n+3), x, n):
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 19 2019

Formula

a(n) = [x^n] Product_{i=1..n+3} (prime(i)*x-1).

a(n) = -abs(A070918(n+3,3)).

a(n) = -abs(A238146(n+3,n)) for n>0.

a(n) = -A260613(n+3,n).