A309804 a(n) is the coefficient of x^n in the polynomial Product_{i=1..n+4} (prime(i)*x-1).

1, 28, 652, 16186, 414849, 11970750, 411154568, 14802996860, 617651235401, 28112591190218, 1330940558814492, 68134228016658366, 3888046744502816953, 244783216404832868510, 15878401438954693327808, 1123935467586630569656024, 83970858613393528568199649

Offset: 0

Author

Alexey V. Bazhin, Aug 17 2019

Keywords

• nonn
• easy

Crossrefs

Cf. A000040, A002110, A024451, A070918, A309802, A309803, A033999, A007504, A024447, A024448, A024449, A054640, A005867, A238146, A260613.

Programs

Maple

a:= n-> coeff(mul(ithprime(i)*x-1, i=1..n+4), x, n):
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 19 2019

Mathematica

a[n_] := CoefficientList[Series[Product[Prime[i]*x - 1, {i, 1, n+4}], {x, 0, 25}], x] [[n+1]]; Array[a, 17, 0] (* Amiram Eldar, Aug 24 2019 *)

PARI

a(n) = polcoef(prod(i=1, n+4, prime(i)*x-1), n); \\ Michel Marcus, Aug 25 2019

Formula

a(n) = [x^n] Product_{i=1..n+4} (prime(i)*x-1).

a(n) = abs(A070918(n+4,4)).

a(n) = abs(A238146(n+4,n)) for n>0.

a(n) = A260613(n+4,n).