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Search: id:A157612
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| A157612 |
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Number of factorizations of n! into distinct factors. |
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+0
3
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| 1, 1, 1, 2, 5, 16, 57, 253, 1060, 5285, 28762, 191263, 1052276
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OFFSET
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0,4
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COMMENT
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The number of factorizations of (n+1)! into k distinct factors can be arranged into the following triangle.
2! 1;
3! 1,1;
4! 1,3,1;
5! 1,7,7,1;
...
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FORMULA
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a(n) = A045778(A000142(n)).
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EXAMPLE
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3!= 6 = 2*3.
a(3)=2 because there are 2 factorizations of 3!
4!= 24 = 2*12 = 3*8 = 4*6 = 2*3*4.
a(4)=5 because there are 5 factorizations of 4!
5! = 120 (1)
5! = 2*60 = 3*40 = 4*30 = 5*24 = 6*20 = 8*15 = 10*12 (7)
5! = 2*3*20 = 2*4*15 = 2*5*12 = 2*6*10 = 3*4*10 = 3*5*8 = 4*5*6 (7)
5! = 2*3*4*5 (1)
a(5)=16 because there are 16 factorizations of 5!
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CROSSREFS
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Cf. A157017, A157229. See A157836 for continuation of triangle.
Sequence in context: A114296 A121689 A009225 this_sequence A149978 A149979 A019448
Adjacent sequences: A157609 A157610 A157611 this_sequence A157613 A157614 A157615
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KEYWORD
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more,nonn
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AUTHOR
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Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 03 2009
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EXTENSIONS
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a(8)-a(12) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Mar 07 2009
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