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A118052
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Number of partitions of n which contain their signature as a subpartition.
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4
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1, 1, 1, 2, 4, 5, 8, 10, 16, 22, 32, 42, 58, 75, 101, 131, 174, 223, 293, 372, 480, 607, 772, 968, 1220, 1517, 1895, 2345, 2908, 3576, 4408, 5390, 6604, 8038, 9788, 11853, 14366, 17315, 20881, 25070, 30098, 35990, 43034, 51272, 61074, 72522
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OFFSET
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0,4
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COMMENTS
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What is lim_{n->infinity} a(n)/p(n) (where p(n) = A000041(n) is the partition function)? It appears to be converging to something close to 0.8.
The limit must be at least 0.83846 = a(64)/p(64) and is probably closer to 0.9. - Charlie Neder, Aug 30 2018
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LINKS
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EXAMPLE
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For n=3, signature([3]) = [1] is a subpartition of [3], signature([2,1]) = [1^2] is a subpartition of [2,1], but signature([1^3]) = [3] is not a subpartition of [1^3], so a(3)=2.
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CROSSREFS
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KEYWORD
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more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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