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 A114799 Septuple factorial, 7-factorial, n!7, n!!!!!!!, a(n) = n*a(n-7) if n > 1, else 1. 12
 1, 1, 2, 3, 4, 5, 6, 7, 8, 18, 30, 44, 60, 78, 98, 120, 288, 510, 792, 1140, 1560, 2058, 2640, 6624, 12240, 19800, 29640, 42120, 57624, 76560, 198720, 379440, 633600, 978120, 1432080, 2016840, 2756160, 7352640, 14418720, 24710400, 39124800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Many of the terms yield multifactorial primes a(n) + 1, e.g.: a(2) + 1 = 3, a(4) + 1 = 5, a(6) + 1 = 7, a(9) + 1 = 19, a(10) + 1 = 31, a(12) + 1 = 61, a(13) + 1 = 79, a(24) + 1 = 12241, a(25) + 1 = 19801, a(26) + 1 = 29641, a(29) + 1 = 76561, a(31) + 1 = 379441, a(35) + 1 = 2016841, a(36) + 1 = 2756161, ... Equivalently, product of all positive integers <= n congruent to n (mod 7). - M. F. Hasler, Feb 23 2018 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Multifactorial. FORMULA a(n) = 1 for n <= 1, else a(n) = n*a(n-7). Sum_{n>=0} 1/a(n) = A288094. - Amiram Eldar, Nov 10 2020 EXAMPLE a(40) = 40 * a(40-7) = 40 * a(33) = 40 * (33*a(26)) = 40 * 33 * (26*a(19)) = 40 * 33 * 26 * (19*a(12)) = 40 * 33 * 26 * 19 * (12*a(5)) = 40 * 33 * 26 * 19 * 12 5 = 39124800. MAPLE A114799 := proc(n)     option remember;     if n < 1 then         1;     else         n*procname(n-7) ;     end if; end proc: seq(A114799(n), n=0..40) ; # R. J. Mathar, Jun 23 2014 A114799 := n -> product(n-7*k, k=0..(n-1)/7); # M. F. Hasler, Feb 23 2018 MATHEMATICA a[n_]:= If[n<1, 1, n*a[n-7]]; Table[a[n], {n, 0, 40}] (* G. C. Greubel, Aug 20 2019 *) PROG (PARI) A114799(n, k=7)=prod(j=0, (n-1)\k, n-j*k) \\ M. F. Hasler, Feb 23 2018 (MAGMA) b:= func< n | (n lt 8) select n else n*Self(n-7) >; [1] cat [b(n): n in [1..40]]; // G. C. Greubel, Aug 20 2019 (Sage) def a(n):     if (n<1): return 1     else: return n*a(n-7) [a(n) for n in (0..40)] # G. C. Greubel, Aug 20 2019 (GAP) a:= function(n)     if n<1 then return 1;     else return n*a(n-7);     fi;   end; List([0..40], n-> a(n) ); # G. C. Greubel, Aug 20 2019 CROSSREFS Cf. A045754, A084947, A288094. Cf. k-fold factorials: A000142, A001147 (and A000165, A006882), A007559 (and A032031, A008544, A007661), A007696 (and A001813, A008545, A047053, A007662), A008548 (and A052562, A047055, A085157), A085158 (and A008542, A047058, A047657), A045755. Sequence in context: A039050 A250043 A260354 * A055557 A173577 A103205 Adjacent sequences:  A114796 A114797 A114798 * A114800 A114801 A114802 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Feb 18 2006 EXTENSIONS Edited by M. F. Hasler, Feb 23 2018 STATUS approved

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Last modified May 8 12:57 EDT 2021. Contains 343666 sequences. (Running on oeis4.)