A305882 - OEIS

%I #6 Jun 14 2018 20:27:49

%S -2,1,1,4,4,13,16,44,52,112,182,411,620,1318,2142,5148,7676,15228,

%T 27530,58660,98372,207392,364464,763263,1341508,2773990,4923220,

%U 10470948,18510902,37546152,69269976,148419094,258284232,534761242,981480012,2004302204

%N -1 + Product_{n>=1} 1/(1 + a(n)*x^n) = g.f. of A000040 (prime numbers).

%F Product_{n>=1} 1/(1 + a(n)*x^n) = 1 + Sum_{k>=1} prime(k)*x^k.

%F Product_{n>=1} (1 + a(n)*x^n) = Sum_{k>=0} A030018(k)*x^k.

%e 1/((1 - 2*x) * (1 + x^2) * (1 + x^3) * (1 + 4*x^4) * (1 + 4*x^5) * ... * (1 + a(n)*x^n) * ...) =  1 + 2*x + 3*x^2 + 5*x^3 + 7*x^4 + 11*x^5 + ... + A000040(k)*x^k + ...

%Y Cf. A000040, A030010, A030018, A145519, A147541, A147557, A305871, A305881.

%K sign

%O 1,1

%A _Ilya Gutkovskiy_, Jun 13 2018