A300662 Expansion of 1/(1 - x - Sum_{k>=2} prime(k-1)*x^k).

1, 1, 3, 8, 22, 59, 160, 429, 1155, 3105, 8354, 22474, 60457, 162636, 437509, 1176941, 3166097, 8517138, 22912002, 61635707, 165806564, 446037175, 1199887133, 3227823181, 8683185454, 23358686444, 62837334885, 169039070970, 454732963567, 1223279724439, 3290751724917

Offset: 0

Author

Ilya Gutkovskiy, Mar 10 2018

Keywords

• nonn

Comments

Invert transform of A008578.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2327
• N. J. A. Sloane, Transforms

Crossrefs

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

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
     `if`(j=1, 1, ithprime(j-1))*a(n-j), j=1..n))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Mar 10 2018

Mathematica

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

Formula

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