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.

A159870 Numerator of Hermite(n, 6/23).

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%I A159870 #14 Sep 08 2022 08:45:44
%S A159870 1,12,-914,-36360,2464716,183452112,-10836922296,-1294597074528,
%T A159870 64723081629840,11734146618363072,-475483423858979616,
%U A159870 -129853072308589057152,3975439219167736085184,1696319876659859502624000,-34322352500514728084132736,-25537758243092015689876280832
%N A159870 Numerator of Hermite(n, 6/23).
%H A159870 G. C. Greubel, <a href="/A159870/b159870.txt">Table of n, a(n) for n = 0..385</a>
%F A159870 From _G. C. Greubel_, Jul 14 2018: (Start)
%F A159870 a(n) = 23^n * Hermite(n, 6/23).
%F A159870 E.g.f.: exp(12*x - 529*x^2).
%F A159870 a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(12/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
%e A159870 Numerators of 1, 12/23, -914/529, -36360/12167, 2464716/279841
%t A159870 Numerator[Table[HermiteH[n, 6/23], {n, 0, 30}]] (* _Vladimir Joseph Stephan Orlovsky_, Jun 22 2011 *)
%t A159870 Table[23^n*HermiteH[n, 6/23], {n,0,30}] (* _G. C. Greubel_, Jul 14 2018 *)
%o A159870 (PARI) a(n)=numerator(polhermite(n, 6/23)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o A159870 (PARI) x='x+O('x^30); Vec(serlaplace(exp(12*x - 529*x^2))) \\ _G. C. Greubel_, Jul 14 2018
%o A159870 (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(12/23)^(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 A159870 Cf. A009967 (denominators)
%K A159870 sign,frac
%O A159870 0,2
%A A159870 _N. J. A. Sloane_, Nov 12 2009