A074142 a(n) is the coefficient of x^n in x/(1 + Sum_{k>=1} (1/2)*(prime(k+1) - 1)*x^k).

1, -1, -1, 0, 0, 2, 1, 0, -2, -5, 2, 3, 5, 6, -10, -12, -9, 11, 32, 11, -5, -55, -61, 29, 84, 129, 9, -188, -232, -136, 322, 567, 255, -354, -1185, -840, 585, 2038, 2318, -594, -3909, -4761, -929, 7387, 10441, 3930, -11137, -23097, -12215, 16547, 44716, 36786, -23108

Offset: 1

Author

Zak Seidov, Sep 16 2002

Keywords

• easy
• sign

Comments

The series reciprocal to the series with coefficients in A005097 has (integer) coefficients with irregular signs and values. In contrast the series reciprocal to the series with coefficients = primes themselves has coefficients (A030018) with alternating signs and regular growth. The radius of convergence (defined from consecutive coefficients ratio) of that series is 0.686777834460.

Crossrefs

Cf. A005097, A030018.

Formula

G.f.: x / (1 + Sum_{i>=1} A005097(i)*x^i).