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%I M4291 N1794 #39 Sep 08 2022 08:44:29
%S 6,96,1200,14400,176400,2257920,30481920,435456000,6586272000,
%T 105380352000,1780927948800,31732897996800,594991837440000,
%U 11716762337280000,241867451105280000,5224336943874048000,117874102296158208000,2773508289321369600000
%N a(n) = n! * binomial(n,3).
%C Coefficients of Laguerre polynomials.
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001805/b001805.txt">Table of n, a(n) for n = 3..100</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F E.g.f.: x^3/(1-x)^4. - _Geoffrey Critzer_, Aug 19 2012
%p G(x):=x^3/(1-x)^4: f[0]:=G(x): for n from 1 to 18 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=3..18); # _Zerinvary Lajos_, Apr 01 2009
%t Table[n! Binomial[n,3], {n,3,30}] (* _Harvey P. Dale_, Feb 23 2011 *)
%o (PARI) for(n=3, 30, print1(n!*binomial(n,3), ", ")) \\ _G. C. Greubel_, May 17 2018
%o (Magma) [Factorial(n)*Binomial(n,3): n in [3..30]]; // _G. C. Greubel_, May 17 2018
%Y Essentially a column of triangle A021012.
%K nonn
%O 3,1
%A _N. J. A. Sloane_
%E More terms from _Ralf Stephan_, Jan 09 2004
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