Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #24 Dec 05 2022 18:02:07
%S 1,40,718,-41840,-3573428,4674400,15945793480,613094814400,
%T -73925536369520,-7283018465187200,295500169093761760,
%U 76056229626701574400,175306544520386380480,-797966872588194008230400,-33928739742998510567799680,8496145352999079190916992000
%N Numerator of Hermite(n, 20/21).
%H DLMF <a href="https://dlmf.nist.gov/18.9">Digital library of mathematical functions</a>, Table 18.9.1 for H_n(x)
%F E.g.f.: exp(-x*(441*x-40)). - _Vincenzo Librandi_, Jan 20 2017
%F D-finite with recurrence a(n) = 40*a(n-1)-882*(n-1)*a(n-2). - [DLMF] _Vincenzo Librandi_, Jan 20 2017, corrected Feb 06 2021
%e Numerators of 1, 40/21, 718/441, -41840/9261, -3573428/194481, ...
%t HermiteH[Range[0,20],20/21]//Numerator (* _Harvey P. Dale_, Dec 05 2022 *)
%o (PARI) a(n)=numerator(polhermite(n, 20/21)) \\ _Charles R Greathouse IV_, Jan 29 2016
%Y Cf. A009965 (denominators).
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009