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

1,4

Comments

By "proper integer partition", one means that the case {n} is excluded for having only one part, equal to the number partitioned.

The growth of this function is exponential a(n) -> c * exp(n).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..70

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.

Example

a(6) = (a(5)+a(1)) + (a(4)+a(2)) + (a(3)+a(2)+a(1)) = (4+1) + (2+0) + (1+0+1) = 9.

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}]

Crossrefs

Cf. A000041, A214948, A000009.

Sequence in context: A024736 A024562 A087219 * A360871 A199296 A219229

Adjacent sequences: A214949 A214950 A214951 * A214953 A214954 A214955

Keyword

nonn

Author

Olivier Gérard, Jul 30 2012

Status

approved