%I #7 Mar 15 2018 18:19:08

%S 1,1,3,8,22,59,160,429,1155,3105,8354,22474,60457,162636,437509,

%T 1176941,3166097,8517138,22912002,61635707,165806564,446037175,

%U 1199887133,3227823181,8683185454,23358686444,62837334885,169039070970,454732963567,1223279724439,3290751724917

%N Expansion of 1/(1 - x - Sum_{k>=2} prime(k-1)*x^k).

%C Invert transform of A008578.

%H Alois P. Heinz, <a href="/A300662/b300662.txt">Table of n, a(n) for n = 0..2327</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F G.f.: 1/(1 - Sum_{k>=1} A008578(k)*x^k).

%p a:= proc(n) option remember; `if`(n=0, 1, add(

%p `if`(j=1, 1, ithprime(j-1))*a(n-j), j=1..n))

%p end:

%p seq(a(n), n=0..35); # _Alois P. Heinz_, Mar 10 2018

%t nmax = 30; CoefficientList[Series[1/(1 - x - Sum[Prime[k - 1] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

%t p[1] = 1; p[n_] := p[n] = Prime[n - 1]; a[n_] := a[n] = Sum[p[k] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 30}]

%Y Cf. A000040, A008578, A023626, A030011, A030012, A030013, A030014, A030015, A030016, A030017, A030018, A292744, A300632.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 10 2018