%I #32 Mar 23 2022 13:00:44

%S 1,-1,1,-2,3,-5,8,-12,19,-31,49,-78,124,-196,312,-497,789,-1254,1993,

%T -3166,5033,-8000,12712,-20202,32106,-51023,81090,-128872,204804,

%U -325483,517271,-822064,1306457,-2076267,3299672,-5243962,8333895,-13244521,21048672,-33451302,53162003

%N Expansion of g.f.: 1/Sum_{p prime} x^p.

%F a(-2) = 1; a(n) = -Sum_{k=1..n+2} A010051(k+2) * a(n-k).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/sum(k=1, N, isprime(k)*x^k))

%o (PARI) a(n) = if(n==-2, 1, -sum(k=1, n+2, isprime(k+2)*a(n-k)));

%Y Cf. A000040, A023360, A040976, A307977, A352479.

%Y Cf. A352500, A010051, A073610, A098238, A340960, A340961, A340962, A340963, A340964, A340965, A340966.

%K sign

%O -2,4

%A _Seiichi Manyama_, Mar 17 2022