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a(0) = 1; for n > 0, a(n) = n!*4^n/2.
4

%I #34 Oct 19 2024 18:27:21

%S 1,2,16,192,3072,61440,1474560,41287680,1321205760,47563407360,

%T 1902536294400,83711596953600,4018156653772800,208944145996185600,

%U 11700872175786393600,702052330547183616000,44931349155019751424000

%N a(0) = 1; for n > 0, a(n) = n!*4^n/2.

%C For n <= 16, denominators in expansion of W(exp(x)) about x=1, where W is the Lambert function.

%H G. C. Greubel, <a href="/A051711/b051711.txt">Table of n, a(n) for n = 0..365</a>

%H J. M. Borwein and R. M. Corless, <a href="https://wayback.cecm.sfu.ca/projects/IntegerRelations/MAA/emerging98.html">Emerging tools for experimental mathematics</a>.

%H J. M. Borwein and R. M. Corless, <a href="http://www.jstor.org/stable/2589743">Emerging tools for experimental mathematics</a>, Amer. Math. Monthly, 106 (No. 10, 1999), 889-909.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=647">Encyclopedia of Combinatorial Structures 647</a>

%F E.g.f.: (1-2*x)/(1-4*x).

%F a(n) = 4*n * a(n-1), n > 0.

%e W(exp(x)) = 1 + (x-1)/2 + (x-1)^2/16 - (x-1)^3/192 - ... .

%t Join[{1},Table[(n! 4^n)/2,{n,20}]] (* _Harvey P. Dale_, Oct 05 2012 *)

%o (PARI) a(n)=if(n<1,!n,4^n/2*n!)

%o (Magma) [1] cat [2^(2*n-1)*Factorial(n): n in [1..30]]; // _G. C. Greubel_, Mar 06 2018

%Y Cf. A001662.

%K nonn,easy,nice,frac,changed

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _James A. Sellers_, Dec 07 1999

%E Edited by _Michael Somos_, Aug 21 2002