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A214952 a(n) is the sum over all proper integer partitions with distinct parts of n of the previous terms. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A199296 A219229 A091620

Adjacent sequences:  A214949 A214950 A214951 * A214953 A214954 A214955

KEYWORD

nonn

AUTHOR

Olivier Gérard, Jul 30 2012

STATUS

approved

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Last modified April 19 08:44 EDT 2019. Contains 322241 sequences. (Running on oeis4.)