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 A034177 a(n) = n-th quartic factorial number divided by 4. 17
 1, 8, 96, 1536, 30720, 737280, 20643840, 660602880, 23781703680, 951268147200, 41855798476800, 2009078326886400, 104472072998092800, 5850436087893196800, 351026165273591808000, 22465674577509875712000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..365 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 513 Norihiro Nakashima, Shuhei Tsujie, Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species, arXiv:1904.09748 [math.CO], 2019. FORMULA 4*a(n) = (4*n)(!^4) = product_{j=1..n} 4*j = 4^n * n!. E.g.f.: (-1 + 1/(1-4*x))/4. EXAMPLE G.f. = x + 8*x^2 + 96*x^3 + 1536*x^4 + 30720*x^5 + 737820*x^6 + ... MAPLE [seq(n!*4^(n-1), n=1..16)]; # Zerinvary Lajos, Sep 23 2006 MATHEMATICA Array[4^(# - 1) #! &, 16] (* Michael De Vlieger, May 30 2019 *) PROG (PARI) vector(20, n, 4^(n-1)*n!) \\ G. C. Greubel, Aug 15 2019 (MAGMA) [4^(n-1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 15 2019 (Sage) [4^(n-1)*factorial(n) for n in (1..20)] # G. C. Greubel, Aug 15 2019 (GAP) List([1..20], n-> 4^(n-1)*Factorial(n) ); # G. C. Greubel, Aug 15 2019 CROSSREFS Cf. A007696, A000407, A034176. First column of triangle A048786. A052570 is an essentially identical sequence. - Philippe Deléham, Sep 18 2008 Equals the second right hand column of A167569 divided by 2. - Johannes W. Meijer, Nov 12 2009 Sequence in context: A260627 A098430 A220285 * A052570 A002168 A114425 Adjacent sequences:  A034174 A034175 A034176 * A034178 A034179 A034180 KEYWORD easy,nonn AUTHOR STATUS approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)