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 A160303 #21 Sep 08 2022 08:45:45 %S A160303 1,10,-1822,-56660,9939052,534992600,-90164363720,-7071178300400, %T A160303 1142359566484880,120150033211799200,-18559035448937462240, %U A160303 -2494873992820155246400,367426387533234274214080,61216037645736403345110400,-8568355342448027542061898880 %N A160303 Numerator of Hermite(n, 5/31). %H A160303 G. C. Greubel, <a href="/A160303/b160303.txt">Table of n, a(n) for n = 0..368</a> %F A160303 a(n+2) = 10*a(n+1) - 1922*(n+1)*a(n). - _Bruno Berselli_, Mar 28 2018 %F A160303 From _G. C. Greubel_, Oct 04 2018: (Start) %F A160303 a(n) = 31^n * Hermite(n, 5/31). %F A160303 E.g.f.: exp(10*x - 961*x^2). %F A160303 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/31)^(n-2*k)/(k!*(n-2*k)!)). (End) %e A160303 Numerators of 1, 10/31, -1822/961, -56660/29791, 9939052/923521, ... %t A160303 Numerator/@HermiteH[Range[0, 20], 5/31] (* _Harvey P. Dale_, May 14 2011 *) %t A160303 Table[31^n*HermiteH[n, 5/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *) %o A160303 (PARI) a(n)=numerator(polhermite(n, 5/31)) \\ _Charles R Greathouse IV_, Jan 29 2016 %o A160303 (PARI) x='x+O('x^30); Vec(serlaplace(exp(10*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018 %o A160303 (Maxima) makelist(num(hermite(n, 5/31)), n, 0, 20); /* _Bruno Berselli_, Mar 28 2018 */ %o A160303 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/31)^(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 A160303 Cf. A009975 (denominators). %K A160303 sign,frac %O A160303 0,2 %A A160303 _N. J. A. Sloane_, Nov 12 2009