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A007662
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Quadruple factorial numbers n!!!!: a(n) = n*a(n-4).
(Formerly M0534)
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22
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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, 2642411520, 4996616625
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OFFSET
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0,3
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REFERENCES
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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
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Klaus Brockhaus, Table of n, a(n) for n = 0..500
Eric Weisstein's World of Mathematics, Multifactorial
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MATHEMATICA
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NFactorialM[n_Integer, m_Integer] := Block[{k = n, p = Max[1, n]}, While[k > m, k -= m; p *= k]; p]; Table[ NFactorialM[n, 4], {n, 0, 34}] (* Robert G. Wilson v *)
With[{k = 4}, Table[With[{q = Quotient[n + k - 1, k]}, k^q q! Binomial[n/k, q]], {n, 0, 34}]] (* Jan Mangaldan, Mar 21 2013 *)
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PROG
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(MAGMA) I:=[ 1, 1, 2, 3 ]; [ n le 4 select I[n] else (n-1)*Self(n-4): n in [1..36] ]; // Klaus Brockhaus, Jun 23 2011
(MAGMA) A007662:=func< n | n eq 0 select 1 else &*[ k: k in [1..n] | k mod 4 eq n mod 4 ] >; [ A007662(n): n in [0..35] ]; // Klaus Brockhaus, Jun 23 2011
(PARI) a(n)=if(n<6, max(n, 1), n*a(n-4)) \\ Charles R Greathouse IV, Jun 23 2011
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CROSSREFS
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Cf. A047053, A007696, A001813, A008545, A000142, A006882, A007661.
Sequence in context: A117577 A069469 A109849 * A175807 A165303 A109744
Adjacent sequences: A007659 A007660 A007661 * A007663 A007664 A007665
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v, Mira Bernstein (mira(AT)math.berkeley.edu)
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STATUS
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approved
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