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

0,2

Links

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

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 *)

Crossrefs

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

Sequence in context: A058696 A134508 A091357 * A129715 A024493 A130781

Adjacent sequences: A309947 A309948 A309949 * A309951 A309952 A309953

Keyword

nonn

Author

Alois P. Heinz, Aug 24 2019

Status

approved