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

%I A349488 #32 Mar 11 2022 09:53:15
%S A349488 0,1,2,6,16,45,115,296,733,1801,4338,10380,24531,57622,134317,311465,
%T A349488 718297,1649579,3772448,8597284,19527774,44225665,99885035,225032910,
%U A349488 505797776,1134419571,2539173978,5672736196,12650878942,28165845957,62609097765,138963709623
%N A349488 Number of unlabeled disconnected P-series with n elements.
%H A349488 Alois P. Heinz, <a href="/A349488/b349488.txt">Table of n, a(n) for n = 1..3217</a>
%F A349488 a(n) = A349276(n) - A255047(n-1).
%p A349488 b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(d*
%p A349488       max(1, 2^(d-1)-1), d=numtheory[divisors](j)), j=1..n)/n)
%p A349488     end:
%p A349488 a:= n-> b(n)-max(1, 2^(n-1)-1):
%p A349488 seq(a(n), n=1..35);  # _Alois P. Heinz_, Jan 05 2022
%t A349488 b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j]*Sum[d*
%t A349488      Max[1, 2^(d-1) - 1], {d, Divisors[j]}], {j, 1, n}]/n];
%t A349488 a[n_] := b[n] - Max[1, 2^(n-1)-1];
%t A349488 Table[a[n], {n, 1, 35}] (* _Jean-François Alcover_, Mar 11 2022, _Alois P. Heinz_ *)
%Y A349488 Cf. A255047, A349276.
%K A349488 nonn
%O A349488 1,3
%A A349488 _Salah Uddin Mohammad_, Nov 19 2021