

A034177


a(n) = nth quartic factorial number divided by 4.


17



1, 8, 96, 1536, 30720, 737280, 20643840, 660602880, 23781703680, 951268147200, 41855798476800, 2009078326886400, 104472072998092800, 5850436087893196800, 351026165273591808000, 22465674577509875712000
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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/(14*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^(n1), 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^(n1)*n!) \\ G. C. Greubel, Aug 15 2019
(MAGMA) [4^(n1)*Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 15 2019
(Sage) [4^(n1)*factorial(n) for n in (1..20)] # G. C. Greubel, Aug 15 2019
(GAP) List([1..20], n> 4^(n1)*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

Wolfdieter Lang


STATUS

approved



