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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.

D-finite with recurrence: a(n) -4*n*a(n-1)=0. - R. J. Mathar, Feb 24 2020

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

Wolfdieter Lang

STATUS

approved

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Last modified November 28 12:15 EST 2020. Contains 338720 sequences. (Running on oeis4.)