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Search: id:A114347
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| A114347 |
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Cumulative sum of triple factorial numbers a(n) = n!!! (A007661). |
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+0
7
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| 1, 2, 4, 7, 11, 21, 39, 67, 147, 309, 589, 1469, 3413, 7053, 19373, 48533, 106773, 316213, 841093, 1947653, 6136453, 17158933, 41503253, 137845653, 402385173, 1010993173, 3515895573, 10658462613, 27699486613, 100341656213
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Triple factorial numbers n!!! = n*(n-3)!!!, 0!!! = 1!!! = 1, 2!!! = 2. The cumulative sum a(n) is prime for n = 1, 3, 4, 7, 12, 14, 15, 17, 19. The cumulative sum a(n) is semiprime for n = 2, 5, 6, 9, 10, 11, 13, 16, 18, 20, 22, 26, 28, 29.
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REFERENCES
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J. Spanier and K. B. Oldham, An Atlas of Functions, Hemisphere, NY, 1987, p. 23.
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FORMULA
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a(n) = SUM[from i = 0 to n] i!!!. a(n) = SUM[from i = 0 to n] A007661(i).
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EXAMPLE
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a(29) = 1 + 1 + 2 + 3 + 4 + 10 + 18 + 28 + 80 + 162 + 280 + 880 + 1944 + 3640 + 12320 + 29160 + 58240 + 209440 + 524880 + 1106560 + 4188800 + 11022480 + 24344320 + 96342400 + 264539520 + 608608000 + 2504902400 + 7142567040 + 17041024000 + 726421696 = 100341656213 = 79 * 1270147547.
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CROSSREFS
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Cf. A000040, A001358, A007661.
Sequence in context: A146156 A024927 A018077 this_sequence A071250 A084992 A058103
Adjacent sequences: A114344 A114345 A114346 this_sequence A114348 A114349 A114350
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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 08 2006
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