A309802 a(n) is the coefficient of x^n in the polynomial Product_{i=1..n+2} (prime(i)*x-1).

1, 10, 101, 1358, 20581, 390238, 8130689, 201123530, 6166988769, 201097530280, 7754625545261, 329758834067168, 14671637258193181, 711027519310719868, 38706187989054920001, 2338431642812927422310, 145908145906128304198449, 9976861293427674211625032

Offset: 0

Author

Alexey V. Bazhin, Aug 17 2019

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000040, A002110, A024451, A070918, A309803, A309804, A033999, A007504, A024447, A024448, A024449, A054640, A005867, A238146, A260613.

Programs

Maple

a:= n-> coeff(mul(ithprime(i)*x-1, i=1..n+2), x, n):
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 18 2019

Formula

a(n) = [x^n] Product_{i=1..n+2} (prime(i)*x-1).

a(n) = abs(A070918(n+2,2)).

a(n) = abs(A238146(n+2,n)) for n>0.

a(n) = A260613(n+2,n).