This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A160328 #13 Sep 08 2022 08:45:45 %S A160328 1,40,-322,-166640,-4808948,1088770400,89764806280,-8965108001600, %T A160328 -1566300023755120,75195499682396800,30101677798211937760, %U A160328 -241190391967188985600,-646057287688484347545920,-20279476307208127137958400,15331208337896144822264021120 %N A160328 Numerator of Hermite(n, 20/31). %H A160328 G. C. Greubel, <a href="/A160328/b160328.txt">Table of n, a(n) for n = 0..368</a> %F A160328 From _G. C. Greubel_, Oct 04 2018: (Start) %F A160328 a(n) = 31^n * Hermite(n, 20/31). %F A160328 a(n+2) = 40*a(n+1) - 1922*(n+1)*a(n) %F A160328 E.g.f.: exp(40*x - 961*x^2). %F A160328 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(40/31)^(n-2*k)/(k!*(n-2*k)!)). (End) %e A160328 Numerators of 1, 40/31, -322/961, -166640/29791, -4808948/923521, ... %t A160328 Table[31^n*HermiteH[n, 20/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *) %o A160328 (PARI) a(n)=numerator(polhermite(n, 20/31)) \\ _Charles R Greathouse IV_, Jan 29 2016 %o A160328 (PARI) x='x+O('x^30); Vec(serlaplace(exp(40*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018 %o A160328 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(40/31)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Oct 04 2018 %Y A160328 Cf. A009975 (denominators). %K A160328 sign,frac %O A160328 0,2 %A A160328 _N. J. A. Sloane_, Nov 12 2009