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A157612
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Number of factorizations of n! into distinct factors.
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2
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1, 1, 1, 2, 5, 16, 57, 253, 1060, 5285, 28762, 191263, 1052276
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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
| a(n) = A045778(A000142(n)).
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EXAMPLE
| 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
| Cf. A157017, A157229. See A157836 for continuation of triangle.
Sequence in context: A121689 A192635 A009225 * A184943 A184596 A149978
Adjacent sequences: A157609 A157610 A157611 * A157613 A157614 A157615
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KEYWORD
| more,nonn
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AUTHOR
| Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 03 2009
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EXTENSIONS
| a(8)-a(12) from Ray Chandler (rayjchandler(AT)sbcglobal.net), Mar 07 2009
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