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%I M5257 N2289 #45 Aug 09 2022 02:29:36
%S 1,36,882,18816,381024,7620480,153679680,3161410560,66784798080,
%T 1454424491520,32724551059200,761589551923200,18341615042150400,
%U 457129482588979200,11787410229615820800,314330939456421888000,8663746518767628288000,246661959710796005376000
%N 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 Cornelius Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 519.
%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="/A001812/b001812.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 Cornelius Lanczos, <a href="/A002457/a002457.pdf">Applied Analysis</a> (Annotated scans of selected pages)
%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>.
%F a(n) = (-1)*A021009(n, 5), n >= 5.
%F a(n) = ((n!/5!)^2)/(n-5)!, n >= 5.
%F If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} (binomial(k,j)* Stirling1(n,k) * Stirling2(j,i)*x^(k-j) then a(n) = (-1)^(n-1)*f(n,5,-6), (n>=5). - _Milan Janjic_, Mar 01 2009
%F From _Amiram Eldar_, May 02 2022: (Start)
%F Sum_{n>=5} 1/a(n) = 375*(gamma - Ei(1)) + 150*e + 175/2, where e = A001113, gamma = A001620, and Ei(1) = A091725.
%F Sum_{n>=5} (-1)^(n+1)/a(n) = 5225*(gamma - Ei(-1)) - 3100/e - 18125/6, where Ei(-1) = -A099285. (End)
%e G.f. = x^5 + 36*x^6 + 882*x^7 + 18816*x^8 + 381024*x^9 + 7620480*x^10 + ...
%t Table[((n!/5!)^2)/(n-5)!, {n, 5, 20}] (* _T. D. Noe_, Aug 10 2012 *)
%o (Sage) [factorial(m) * binomial(m, 5) / 120 for m in range(5,23)] # _Zerinvary Lajos_, Jul 05 2008
%o (PARI) for(n=5,20, print1(((n!/5!)^2)/(n-5)!, ", ")) \\ _G. C. Greubel_, May 11 2018
%o (Magma) [((Factorial(n)/Factorial(5))^2)/Factorial(n-5): n in [5..20]]; // _G. C. Greubel_, May 11 2018
%Y Cf. A001113, A001620, A021009, A091725, A099285.
%K nonn
%O 5,2
%A _N. J. A. Sloane_
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