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 A045754 7-fold factorials: a(n) = Product_{k=0..n-1} (7*k+1). 34
 1, 1, 8, 120, 2640, 76560, 2756160, 118514880, 5925744000, 337767408000, 21617114112000, 1534815101952000, 119715577952256000, 10175824125941760000, 936175819586641920000, 92681406139077550080000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..338 FORMULA a(n) = Sum_{k=0..n} (-7)^(n-k)*A048994(n, k), where A048994 = Stirling-1 numbers. E.g.f.: (1-7*x)^(-1/7). G.f.: 1/(1-x/(1-7*x/(1-8*x/(1-14*x/(1-15*x/(1-21*x/(1-22*x/(1-... (continued fraction). - Philippe Deléham, Jan 08 2012 a(n) = (-6)^n*Sum_{k=0..n} (7/6)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012 G.f.: 1/G(0), where G(k)= 1 - x*(7*k+1)/(1 - x*(7*k+7)/G(k+1)); (continued fraction). - Sergei N. Gladkovskii, Jun 05 2013 G.f.: G(0)/2, where G(k)= 1 + 1/(1 - x*(7*k+1)/(x*(7*k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 05 2013 a(n) = 7^n * Gamma(n + 1/7) / Gamma(1/7). - Artur Jasinski, Aug 23 2016 a(n) = A114799(7n-6). - M. F. Hasler, Feb 23 2018 D-finite with recurrence: a(n) +(-7*n+6)*a(n-1)=0. - R. J. Mathar, Jan 17 2020 MAPLE f := n->product( (7*k+1), k=0..(n-1)); G(x):=(1-7*x)^(-1/7): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..14); # Zerinvary Lajos, Apr 03 2009 MATHEMATICA FoldList[Times, 1, 7Range[0, 20] + 1] (* Harvey P. Dale, Jan 21 2013 *) PROG (PARI) a(n)=prod(k=0, n-1, 7*k+1) (MAGMA) [1] cat [&*[7*j+1: j in [0..n-1]]: n in [1..20]]; // G. C. Greubel, Aug 21 2019 (Sage) [7^n*rising_factorial(1/7, n) for n in (0..20)] # G. C. Greubel, Aug 21 2019 (GAP) List([0..20], n-> Product([0..n-1], k-> 7*k+1) ); # G. C. Greubel, Aug 21 2019 CROSSREFS 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), A008542 (and A085158), A045755. See also A113134. Unsigned row sums of triangle A051186 (scaled Stirling1). First column of triangle A132056 (S2(8)). Cf. A114799, A084947, A144739, A144827, A147585, A049209, A051188. Sequence in context: A211825 A113383 A218671 * A339201 A229045 A173774 Adjacent sequences:  A045751 A045752 A045753 * A045755 A045756 A045757 KEYWORD nonn AUTHOR EXTENSIONS Additional comments from Philippe Deléham and Paul D. Hanna, Oct 29 2005 Edited by N. J. A. Sloane, Oct 16 2008 at the suggestion of M. F. Hasler, Oct 14 2008 Corrected by Zerinvary Lajos, Apr 03 2009 STATUS approved

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Last modified April 11 22:01 EDT 2021. Contains 342888 sequences. (Running on oeis4.)