A309950 G.f.: Product_{j>=1} (1 + p(x^j)), where p(x) is the g.f. of A000040.

1, 2, 5, 11, 22, 43, 78, 140, 238, 405, 665, 1077, 1710, 2685, 4140, 6336, 9551, 14280, 21117, 30994, 45051, 65046, 93170, 132600, 187439, 263449, 367999, 511409, 706833, 972257, 1330929, 1813846, 2461090, 3325803, 4476276, 6002036, 8018216, 10674307, 14161656

Offset: 0

Author

Alois P. Heinz, Aug 24 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000040, A006171, A008578, A162891, A309955.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i=1, ithprime(n),
      add(b(j, 1)*(t-> b(t, min(t, i-1)))(n-i*j), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..40);

Mathematica

b[n_, i_] := b[n, i] = If[n==0, 1, If[i==1,
   Prime[n], Sum[b[j, 1]*Function[t,
   b[t, Min[t, i-1]]][n-i*j], {j, 0, n/i}]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Sep 15 2022, after Alois P. Heinz *)