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 A160317 #15 Sep 08 2022 08:45:45 %S A160317 1,38,-478,-164236,-3484820,1130223208,76437602104,-10129105154704, %T A160317 -1413297494585968,102039816064461920,28324733071797627424, %U A160317 -884865408030648260288,-632466392109110072889152,-3625187129327311294505344,15665048162323786452017148800 %N A160317 Numerator of Hermite(n, 19/31). %H A160317 G. C. Greubel, <a href="/A160317/b160317.txt">Table of n, a(n) for n = 0..368</a> %F A160317 From _G. C. Greubel_, Oct 04 2018: (Start) %F A160317 a(n) = 31^n * Hermite(n, 19/31). %F A160317 a(n+2) = 38*a(n+1) - 1922*(n+1)*a(n) %F A160317 E.g.f.: exp(38*x - 961*x^2). %F A160317 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(38/31)^(n-2*k)/(k!*(n-2*k)!)). (End) %e A160317 Numerators of 1, 38/31, -478/961, -164236/29791, -3484820/923521, ... %t A160317 Numerator[HermiteH[Range[0,20],19/31]] (* _Harvey P. Dale_, Dec 26 2017 *) %t A160317 Table[31^n*HermiteH[n, 19/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *) %o A160317 (PARI) a(n)=numerator(polhermite(n, 19/31)) \\ _Charles R Greathouse IV_, Jan 29 2016 %o A160317 (PARI) x='x+O('x^30); Vec(serlaplace(exp(38*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018 %o A160317 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(38/31)^(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 A160317 Cf. A009975 (denominators). %K A160317 sign,frac %O A160317 0,2 %A A160317 _N. J. A. Sloane_, Nov 12 2009