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 A160315 #15 Sep 08 2022 08:45:45 %S A160315 1,34,-766,-156740,-912404,1173995384,48684045496,-11883257221424, %T A160315 -1059025893631600,146710082653141024,23307172718246211616, %U A160315 -2027323916172999286336,-561689258759043381720896,27660764004806580561543040,14974833795516881674770770816 %N A160315 Numerator of Hermite(n, 17/31). %H A160315 G. C. Greubel, <a href="/A160315/b160315.txt">Table of n, a(n) for n = 0..368</a> %F A160315 From _G. C. Greubel_, Oct 04 2018: (Start) %F A160315 a(n) = 31^n * Hermite(n, 17/31). %F A160315 a(n+2) = 34*a(n+1) - 1922*(n+1)*a(n) %F A160315 E.g.f.: exp(34*x - 961*x^2). %F A160315 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(34/31)^(n-2*k)/(k!*(n-2*k)!)). (End) %e A160315 Numerators of 1, 34/31, -766/961, -156740/29791, -912404/923521, ... %t A160315 Numerator[HermiteH[Range[0,20],17/31]] (* _Harvey P. Dale_, Feb 24 2013 *) %t A160315 Table[31^n*HermiteH[n, 17/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *) %o A160315 (PARI) a(n)=numerator(polhermite(n, 17/31)) \\ _Charles R Greathouse IV_, Jan 29 2016 %o A160315 (PARI) x='x+O('x^30); Vec(serlaplace(exp(34*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018 %o A160315 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(34/31)^(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 A160315 Cf. A009975 (denominators). %K A160315 sign,frac %O A160315 0,2 %A A160315 _N. J. A. Sloane_, Nov 12 2009