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Search: id:A114423
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| A114423 |
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Multifactorial array read by antidiagonals. |
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+0
1
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| 1, 2, 1, 6, 2, 1, 24, 3, 2, 1, 120, 8, 3, 2, 1, 720, 15, 4, 3, 2, 1, 5040, 48, 10, 4, 3, 2, 1, 40320, 105, 18, 5, 4, 3, 2, 1, 362880, 384, 28, 12, 5, 4, 3, 2, 1, 3628800, 945, 80, 21, 6, 5, 4, 3, 2, 1, 39916800, 3840, 162, 32, 14, 6, 5, 4, 3, 2, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The upper-left corner of the array of multifactorials, read here by antidiagonals, is:
1!.....1!!....1!!!...1!!!!...
2!.....2!!....2!!!...2!!!!...
3!.....3!!....3!!!...3!!!!...
4!.....4!!....4!!!...4!!!!...
5!.....5!!....5!!!...5!!!!...
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LINKS
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Eric Weisstein's World of Mathematics, Multifactorial.
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FORMULA
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Values by antidiagonal of array M(a,b) = a!b. M(1,n) = (1! = 1, 1!! = 1, 1!!! = 1, 1!!!! = 1, ...). M(2,n) = (2! = 2, 2!! = 2, 2!!! = 2, 2!!!! = 2, ...). M(3,n) = (3! = 6, 3!! = 3, 3!!! = 3, 3!!!! = 3, ...). M(4,n) = (4! = 24, 4!! = 8, 4!!! = 4, 4!!!! = 4, ...). M(5,n) = (5! = 120, 5!! = 15, 5!!! = 10, 5!!!! = 5, ...). M(6,n) = (6! = 720, 6!! = 48, 6!!! = 18, 6!!!! = 12, ...).
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CROSSREFS
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Cf. n!:A000142, n!!:A006882, n!!!:A007661, n!!!!:A007662, n!!!!!!:A085158.
Sequence in context: A114283 A106187 A110135 this_sequence A069123 A134133 A134134
Adjacent sequences: A114420 A114421 A114422 this_sequence A114424 A114425 A114426
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 12 2006
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