A180129 Expansion of log(1/(1-Prime(x))) where Prime(x) = Sum{n>=1} A008578(n)*x^n.

1, 5, 16, 49, 136, 380, 1016, 2745, 7369, 19840, 53395, 143620, 386374, 1039386, 2796001, 7521561, 20233860, 54431237, 146425762, 393900764, 1059634634, 2850529093, 7668224519, 20628334404, 55492399461, 149280418500, 401580100348, 1080292905482, 2906102072179, 7817721667285

Offset: 1

Author

Vladimir Kruchinin, Aug 12 2010

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A008578, A300662.

Programs

PARI

seq(n)={Vec(deriv(log(1/(1 - x - x*sum(k=1, n-1, prime(k)*x^k, O(x^n))))))} \\ Andrew Howroyd, Jan 04 2020

Formula

Logarithm g.f.: Sum_{n>0} a(n)*x^n/n = log(1/(1-Prime(x))).

Logarithmic derivative of A300662. - Andrew Howroyd, Jan 04 2020

Extensions

Terms a(16) and beyond from Andrew Howroyd, Jan 04 2020