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 A160147 #19 Sep 08 2022 08:45:44 %S A160147 1,38,-14,-111340,-4169684,490886888,49050698104,-2430351968272, %T A160147 -592964799643760,5814962971461728,8001852693840964384, %U A160147 219288242242044652352,-120000760298623690001216,-8396695977614513457596800,1955419963550761908894369664 %N A160147 Numerator of Hermite(n, 19/27). %H A160147 G. C. Greubel, <a href="/A160147/b160147.txt">Table of n, a(n) for n = 0..376</a> %F A160147 From _G. C. Greubel_, Sep 24 2018: (Start) %F A160147 a(n) = 27^n * Hermite(n, 19/27). %F A160147 E.g.f.: exp(38*x - 729*x^2). %F A160147 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/27)^(n-2*k)/(k!*(n-2*k)!)). (End) %e A160147 Numerators of 1, 38/27, -14/729, -111340/19683, -4169684/531441, ... %t A160147 Table[27^n*HermiteH[n, 19/27], {n, 0, 30}] (* _G. C. Greubel_, Sep 24 2018 *) %o A160147 (PARI) a(n)=numerator(polhermite(n, 19/27)) \\ _Charles R Greathouse IV_, Jan 29 2016 %o A160147 (PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 729*x^2))) \\ _G. C. Greubel_, Sep 24 2018 %o A160147 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/27)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Sep 24 2018 %Y A160147 Cf. A009971 (denominators). %K A160147 sign,frac %O A160147 0,2 %A A160147 _N. J. A. Sloane_, Nov 12 2009