A214952 a(n) is the sum over all proper integer partitions with distinct parts of n of the previous terms.
1, 0, 1, 2, 4, 9, 20, 44, 100, 225, 507, 1145, 2592, 5858, 13275, 30043, 68054, 154132, 349182, 790954, 1792001, 4059646, 9197535, 20837459, 47209682, 106957699, 242325918, 549015961, 1243864083, 2818122854, 6384811753, 14465578718, 32773596120, 74252685312
Offset: 1
Keywords
Examples
a(6) = (a(5)+a(1)) + (a(4)+a(2)) + (a(3)+a(2)+a(1)) = (4+1) + (2+0) + (1+0+1) = 9.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..70
Programs
-
Mathematica
Clear[a]; a[1] := 1; a[n_Integer] := a[n] = Plus @@ Map[Function[p, Plus @@ Map[a, p]], Select[Drop[IntegerPartitions[n], 1], Union[#]==Sort[#]&]]; Table[ a[n], {n,1,30}]
Formula
a(n) = sum( sum( a(i), i in p) , p in P*(n)) where Q*(n) is the set of all integer partitions of n with distinct parts excluding {n}, p is a partition of Q*(n), i is a part of p.
Comments