A349488 Number of unlabeled disconnected P-series with n elements.

0, 1, 2, 6, 16, 45, 115, 296, 733, 1801, 4338, 10380, 24531, 57622, 134317, 311465, 718297, 1649579, 3772448, 8597284, 19527774, 44225665, 99885035, 225032910, 505797776, 1134419571, 2539173978, 5672736196, 12650878942, 28165845957, 62609097765, 138963709623

Offset: 1

Author

Salah Uddin Mohammad, Nov 19 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..3217

Crossrefs

Cf. A255047, A349276.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(d*
      max(1, 2^(d-1)-1), d=numtheory[divisors](j)), j=1..n)/n)
    end:
a:= n-> b(n)-max(1, 2^(n-1)-1):
seq(a(n), n=1..35);  # Alois P. Heinz, Jan 05 2022

Mathematica

b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j]*Sum[d*
     Max[1, 2^(d-1) - 1], {d, Divisors[j]}], {j, 1, n}]/n];
a[n_] := b[n] - Max[1, 2^(n-1)-1];
Table[a[n], {n, 1, 35}] (* Jean-François Alcover, Mar 11 2022, Alois P. Heinz *)

Formula

a(n) = A349276(n) - A255047(n-1).