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 A160316 #13 Sep 08 2022 08:45:45 %S A160316 1,36,-626,-160920,-2183604,1158543216,62691990216,-11103408719136, %T A160316 -1243180750254960,125971505456256576,26039514814335534816, %U A160316 -1483749801553172137344,-603942415060596074024256,12479278480840903510828800,15539359208014326031959897216 %N A160316 Numerator of Hermite(n, 18/31). %H A160316 G. C. Greubel, <a href="/A160316/b160316.txt">Table of n, a(n) for n = 0..368</a> %F A160316 From _G. C. Greubel_, Oct 04 2018: (Start) %F A160316 a(n) = 31^n * Hermite(n, 18/31). %F A160316 a(n+2) = 36*a(n+1) - 1922*(n+1)*a(n) %F A160316 E.g.f.: exp(36*x - 961*x^2). %F A160316 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/31)^(n-2*k)/(k!*(n-2*k)!)). (End) %e A160316 Numerators of 1, 36/31, -626/961, -160920/29791, -2183604/923521, ... %t A160316 Table[31^n*HermiteH[n, 18/31], {n, 0, 30}] (* _G. C. Greubel_, Oct 04 2018 *) %o A160316 (PARI) a(n)=numerator(polhermite(n, 18/31)) \\ _Charles R Greathouse IV_, Jan 29 2016 %o A160316 (PARI) x='x+O('x^30); Vec(serlaplace(exp(36*x - 961*x^2))) \\ _G. C. Greubel_, Oct 04 2018 %o A160316 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/31)^(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 A160316 Cf. A009975 (denominators). %K A160316 sign,frac %O A160316 0,2 %A A160316 _N. J. A. Sloane_, Nov 12 2009