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 A159005 #13 Sep 08 2022 08:45:43 %S A159005 1,10,2,-1940,-19988,560600,15400120,-175631600,-12320798320, %T A159005 14487191200,11011816030240,95920712926400,-10911530551334720, %U A159005 -221918063914793600,11682109283252497280,421292676523621792000,-12959773881144953081600 %N A159005 Numerator of Hermite(n, 5/7). %H A159005 G. C. Greubel, <a href="/A159005/b159005.txt">Table of n, a(n) for n = 0..450</a> %F A159005 From _G. C. Greubel_, Jul 14 2018: (Start) %F A159005 a(n) = 7^n * Hermite(n, 5/7). %F A159005 E.g.f.: exp(10*x - 49*x^2). %F A159005 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(10/7)^(n-2*k)/(k!*(n-2*k)!)). (End) %t A159005 Numerator[Table[HermiteH[n,5/7],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 01 2011*) %t A159005 Table[7^n*HermiteH[n, 5/7], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *) %o A159005 (PARI) a(n)=numerator(polhermite(n,5/7)) \\ _Charles R Greathouse IV_, Jan 29 2016 %o A159005 (PARI) x='x+O('x^30); Vec(serlaplace(exp(10*x - 49*x^2))) \\ _G. C. Greubel_, Jul 14 2018 %o A159005 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(10/7)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 14 2018 %Y A159005 Cf. A158980. %K A159005 sign,frac %O A159005 0,2 %A A159005 _N. J. A. Sloane_, Nov 12 2009