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a(n) = n! * binomial(n,5).
(Formerly M5380 N2337)
4

%I M5380 N2337 #36 Sep 08 2022 08:44:29

%S 120,4320,105840,2257920,45722880,914457600,18441561600,379369267200,

%T 8014175769600,174530938982400,3926946127104000,91390746230784000,

%U 2200993805058048000,54855537910677504000,1414489227553898496000,37719712734770626560000

%N a(n) = n! * binomial(n,5).

%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="/A001807/b001807.txt">Table of n, a(n) for n = 5..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^5/(1-x)^6. - _Geoffrey Critzer_, Aug 19 2012

%p G(x):=x^5/(1-x)^6: 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=5..18); # _Zerinvary Lajos_, Apr 01 2009

%t Table[n! Binomial[n, 5], {n, 5, 20}] (* _T. D. Noe_, Aug 10 2012 *)

%o (Sage) [binomial(n,5)*factorial (n) for n in range(5, 19)] # _Zerinvary Lajos_, Jul 07 2009

%o (PARI) for(n=5, 35, print1(n!*binomial(n,5), ", ")) \\ _G. C. Greubel_, May 17 2018

%o (Magma) [Factorial(n)*Binomial(n,5): n in [5..35]]; // _G. C. Greubel_, May 17 2018

%Y Essentially a column of triangle A021012.

%K nonn

%O 5,1

%A _N. J. A. Sloane_

%E More terms from _Ralf Stephan_, Jan 09 2004