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A007661
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Triple factorial numbers a(n) = n!!!, defined by a(n) = n*a(n-3), a(0) = a(1) = 1, a(2) = 2.
(Formerly M0596)
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27
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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, 72642169600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The triple factorial of a positive integer n is the product of the positive integers <= n that have the same residue modulo 3 as n. - Peter Luschny, Jun 23 2011
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. Spanier and K. B. Oldham, An Atlas of Functions, Hemisphere, NY, 1987, p. 23.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..200
M. L. Perez, Smarandache k-factorials
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| a(n) = prod(i=0..floor((n-1)/3), n-3*i ) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Feb 16 2008
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MAPLE
| A007661 := n -> mul(k, k = select(k -> k mod 3 = n mod 3, [$1 .. n])): seq(A007661(n), n = 0 .. 29);
- Peter Luschny, Jun 23 2011
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MATHEMATICA
| multiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*multiFactorial[n - k, k]]]; Array[ multiFactorial[#, 3] &, 30, 0] (* Robert G. Wilson v, Apr 23 2011 *)
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PROG
| (PARI) a(n, d=3)=prod(i=0, (n-1)\d, n-d*i) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Feb 16 2008
(PARI) a(n) = prod(i=0, floor((n-1)/3), n-3*i );
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CROSSREFS
| Cf. A000142, A006882 (= A001147 union A000165), A007662.
Sequence in context: A055506 A098088 A080500 * A049891 A135432 A108364
Adjacent sequences: A007658 A007659 A007660 * A007662 A007663 A007664
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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