cp's OEIS Frontend

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.

A159874 Numerator of Hermite(n, 10/23).

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%I A159874 #10 Sep 08 2022 08:45:44
%S A159874 1,20,-658,-55480,978892,254369200,-90954680,-1616554775200,
%T A159874 -31657485143920,13049369914414400,562429971828694240,
%U A159874 -126813734257930467200,-9081834697300952909120,1428390476192666153388800,153479363950530629379812480,-18087732454355158476398656000
%N A159874 Numerator of Hermite(n, 10/23).
%H A159874 G. C. Greubel, <a href="/A159874/b159874.txt">Table of n, a(n) for n = 0..385</a>
%F A159874 From _G. C. Greubel_, Jul 15 2018: (Start)
%F A159874 a(n) = 23^n * Hermite(n, 10/23).
%F A159874 E.g.f.: exp(20*x - 529*x^2).
%F A159874 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A159874 Numerators of 1, 20/23, -658/529, -55480/12167, 978892/279841,...
%t A159874 Numerator[Table[HermiteH[n, 11/23], {n, 0, 30}]] (* or *) Table[23^n* HermiteH[n, 10/23], {n,0,30}] (* _G. C. Greubel_, Jul 15 2018 *)
%o A159874 (PARI) a(n)=numerator(polhermite(n, 10/23)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159874 (PARI) x='x+O('x^30); Vec(serlaplace(exp(20*x - 529*x^2))) \\ _G. C. Greubel_, Jul 15 2018
%o A159874 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(20/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jul 15 2018
%Y A159874 Cf. A009967 (denominators)
%K A159874 sign,frac
%O A159874 0,2
%A A159874 _N. J. A. Sloane_, Nov 12 2009