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%I M4862 N2078 #31 Jun 25 2023 02:41:40
%S 12,120,720,3360,13440,48384,161280,506880,1520640,4392960,12300288,
%T 33546240,89456640,233963520,601620480,1524105216,3810263040,
%U 9413591040,23011000320,55710842880,133706022912,318347673600,752458137600,1766640844800,4122161971200
%N Coefficients of x^n in Hermite polynomial H_{n+4}
%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. 801.
%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="/A001816/b001816.txt">Table of n, a(n) for n = 0..500</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/He#Hermite">Index entries for sequences related to Hermite polynomials</a>.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10, -40, 80, -80, 32).
%F a(n) = 12*A003472(n+4) = A060821(4+n, n).
%F G.f.: 12 ( 1 - 2 x )^(-5).
%F From _Amiram Eldar_, May 06 2022: (Start)
%F Sum_{n>=0} 1/a(n) = 5/9 - 2*log(2)/3.
%F Sum_{n>=0} (-1)^n/a(n) = 18*log(3/2) - 65/9. (End)
%t Table[Coefficient[HermiteH[n + 4, x], x, n], {n, 0, 25}] (* _T. D. Noe_, Aug 10 2012 *)
%o (PARI) a(n) = polcoeff(polhermite(n+4), n); \\ _Michel Marcus_, May 06 2022
%Y Cf. A003472, A060821.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, _Simon Plouffe_
%E More terms from Larry Reeves (larryr(AT)acm.org), Jan 29 2001
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