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A323764 Dirichlet self-convolution of the integer partition numbers A000041. 3
1, 1, 4, 6, 14, 14, 34, 30, 64, 69, 112, 112, 228, 202, 330, 394, 575, 594, 956, 980, 1492, 1674, 2228, 2510, 3700, 3965, 5276, 6200, 8126, 9130, 12318, 13684, 17842, 20622, 25808, 29976, 38377, 43274, 53990, 62976, 77912, 89166, 110656, 126522, 154918, 179744 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Also the number of multiset partitions of constant multiset partitions of integer partitions of n.
LINKS
FORMULA
a(n) ~ exp(Pi*sqrt(2*n/3)) / (2*n*sqrt(3)). - Vaclav Kotesovec, Jan 28 2019
EXAMPLE
The a(4) = 14 multiset partitions of constant multiset partitions:
((1111)) ((22)) ((4)) ((31)) ((211))
((11)(11)) ((2)(2))
((11))((11)) ((2))((2))
((1)(1)(1)(1))
((1))((1)(1)(1))
((1)(1))((1)(1))
((1))((1))((1)(1))
((1))((1))((1))((1))
MATHEMATICA
Join[{1}, Table[Sum[PartitionsP[d]*PartitionsP[n/d], {d, Divisors[n]}], {n, 1, 100}]]
CROSSREFS
Sequence in context: A310604 A310605 A034759 * A310606 A310607 A310608
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 27 2019
STATUS
approved

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Last modified May 19 09:42 EDT 2024. Contains 372683 sequences. (Running on oeis4.)