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A108895
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Partial sums of quadruple factorial numbers n!!!! (A007662).
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0
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1, 2, 4, 7, 11, 16, 28, 49, 81, 126, 246, 477, 861, 1446, 3126, 6591, 12735, 22680, 52920, 118755, 241635, 450480, 1115760, 2629965, 5579085, 10800210, 28097490, 68981025, 151556385, 302969010, 821887410, 2089276995, 4731688515
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Quadruple factorial numbers n!!!! = n*(n-4)!!!!, 0!!!! = 1!!!! = 1, 2!!!! = 2, 3!!!! = 3. The cumulative sum a(n) is prime for n = 1, 3, 4 and never again, as all values from a(8) = 81 are multiples of 3. The cumulative sum a(n) is semiprime for n = 2, 7 and never again, as all values from a(16) are divisible by both 3 and 5.
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REFERENCES
| J. Spanier and K. B. Oldham, An Atlas of Functions, Hemisphere, NY, 1987, p. 23.
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FORMULA
| a(n) = SUM[from i = 0 to n] i!!!!. a(n) = SUM[from i = 0 to n] A007662(i).
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EXAMPLE
| a(31) = 1 + 1 + 2 + 3 + 4 + 5 + 12 + 21 +
32 + 45 + 120 + 231 + 384 + 585 + 1680 + 3465 + 6144 +
9945 + 30240 + 65835 + 122880 + 208845 + 665280 +
1514205 + 2949120 + 5221125 + 17297280 + 40883535 +
82575360 + 151412625 + 518918400 + 1267389585 =
2089276995 = 3 * 5 * 13 * 337 * 31793.
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MATHEMATICA
| NFactorialM[n_Integer, m_Integer] := Block[{k = n, p = Max[1, n]}, While[k > m, k -= m; p *= k]; p]; Table[ Sum[ NFactorialM[i, 4], {i, 0, n}], {n, 0, 33}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 21 2006)
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CROSSREFS
| Cf. A000040, A001358, A007662, A114347.
Sequence in context: A063676 A099385 A120118 * A146929 A146921 A153535
Adjacent sequences: A108892 A108893 A108894 * A108896 A108897 A108898
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 08 2006
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